Perspectivities

This table shows pairs of perspective central triangles and their perspectors. In order to search for the perspector of two triangles, order the names of the triangles alphabetically. For present purposes let U be your first triangle and V the second triangle. Find U in the first column. (If U is missing, then U is not perspective to any other triangle V in the table with V>U). For the chosen U, seek V in the second column. (If V is missing then U is not perspective to V.) Once you find V, you will see a number, k, after it, signifying that X(k) in ETC is the perspector (formerly known as center of perspective) of U and V, unless k = 0, which signifies that the perspector is not in ETC.

Notation:

An asterisk, *, means that the two triangles are homothetic.
A dollar sign, \$, means that the two triangles are directly similar.
The pair "\$-" means that the two triangles are inversely similar.

Certain triangles are known by more than one name. Names used in the table are bolded in the following list:

Caelum triangle = 5th mixtilinear triangle
Carnot triangle = Johnson triangle
circumcircle-midarc triangle = 2nd circumperp triangle
contact triangle = intouch triangle
D-triangle = 4th Brocard triangle
half-altitude triangle = midheight triangle

 U V ABC {Andromeda, 1}, {anti-Brocard (1st)\$-, 1916}, {anticomplementary*, 2}, {Antlia, 1}, {Apus, 55}, {Aquila*, 1}, {Ara*, 25}, {Auriga (1st)*, 5597}, {Auriga (2nd)*, 5598}, {bci, 1127}, {Brocard (1st)\$-, 76}, {Brocard (2nd), 6}, {Brocard (3rd), 32}, {Brocard (4th), 2}, {circummedial, 2}, {circumorthic, 4}, {circumperp (2nd), 1}, {circumsymmedial, 6}, {Euler*, 4}, {Euler (2nd), 68}, {Euler (5th), 2}, {excentral, 1}, {extangents, 65}, {extouch, 8}, {extouch (2nd), 4}, {extouch (3rd), 4}, {extouch (4th), 69}, {extouch (5th), 388}, {Feuerbach, 12}, {Garcia (outer)*, 10}, {Grebe (inner)*, 6}, {Grebe (outer)*, 6}, {hexyl, 84}, {Honsberger, 7}, {Hutson (extouch), 7}, {Hutson (intouch), 8}, {Hutson (outer), 0}, {incentral, 1}, {intouch, 7}, {Johnson*, 5}, {Lemoine, 598}, {Lucas antipodal, 3}, {Lucas Brocard, 6421}, {Lucas central, 3}, {Lucas homothetic*, 493}, {Lucas inner, 1151}, {Lucas inner tangential, 6425}, {Lucas reflection, 6401}, {Lucas secondary central, 6417}, {Lucas secondary tangents (1st), 6419}, {Lucas secondary tangents (2nd), 372}, {Lucas tangents, 371}, {Lucas(-1) antipodal, 3}, {Lucas(-1) Brocard, 6422}, {Lucas(-1) central, 3}, {Lucas(-1) homothetic*, 494}, {Lucas(-1) inner, 1152}, {Lucas(-1) inner tangential, 6426}, {Lucas(-1) reflection, 6402}, {Lucas(-1) secondary central, 6418}, {Lucas(-1) secondary tangents (1st), 6420}, {Lucas(-1) secondary tangents (2nd), 371}, {Lucas(-1) tangents, 372}, {Macbeath, 264}, {McCay, 7607}, {medial*, 2}, {midarc, 1}, {midheight, 4}, {mixtilinear, 1}, {mixtilinear (2nd), 1}, {mixtilinear (3rd), 56}, {mixtilinear (4th), 55}, {mixtilinear (5th)*, 1}, {mixtilinear (6th), 3062}, {Morley (1st), 357}, {Morley (2nd), 1136}, {Morley (3rd), 1134}, {Morley adjunct (1st), 358}, {Morley adjunct (2nd), 1137}, {Morley adjunct (3rd), 1135}, {Napoleon (inner), 18}, {Napoleon (outer), 17}, {Neuberg (1st), 98}, {Neuberg (2nd), 262}, {orthic, 4}, {orthocentroidal\$-, 4}, {Pamfilos-Zhou (1st), 7594}, {Pamfilos-Zhou (2nd), 7595}, {reflection, 4}, {Schroeter, 523}, {Sharygin (1st), 256}, {Sharygin (2nd), 291}, {Soddy (inner), 176}, {Soddy (outer), 175}, {squares (inner), 485}, {squares (outer), 486}, {Steiner, 99}, {symmedial, 6}, {tangential, 6}, {tangential-midarc, 177}, {Trinh, 74}, {Vecten (inner), 486}, {Vecten (outer), 485}, {Yff central, 177}, {Yff contact, 190}, {Yiu, 5} Andromeda {Antlia, 1}, {Aquila, 1}, {circumperp (2nd), 1}, {excentral, 1}, {incentral, 1}, {intouch, 4907}, {medial, 5573}, {midarc, 1}, {mixtilinear, 1}, {mixtilinear (2nd), 1}, {mixtilinear (5th), 1} anti-Brocard (1st) {anticomplementary\$-, 147}, {Brocard (1st)*, 2}, {Brocard (2nd), 2}, {circummedial, 99}, {circumsymmedial, 8289}, {Lucas Brocard, 8302}, {Lucas central, 8304}, {Lucas inner, 8306}, {Lucas inner tangential, 8308}, {Lucas reflection, 0}, {Lucas secondary central, 8310}, {Lucas secondary tangents (1st), 8312}, {Lucas secondary tangents (2nd), 8314}, {Lucas tangents, 8316}, {Lucas(-1) Brocard, 8303}, {Lucas(-1) central, 8305}, {Lucas(-1) inner, 8307}, {Lucas(-1) inner tangential, 8309}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 8311}, {Lucas(-1) secondary tangents (1st), 8313}, {Lucas(-1) secondary tangents (2nd), 8315}, {Lucas(-1) tangents, 8317}, {McCay, 8350}, {medial\$-, 8290}, {Napoleon (inner), 8291}, {Napoleon (outer), 8292}, {Neuberg (1st), 8295}, {Neuberg (2nd), 147}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 1281}, {Sharygin (2nd), 1281}, {symmedial, 4027}, {tangential, 5989}, {Vecten (inner), 8293}, {Vecten (outer), 8294} anticomplementary {Aquila*, 10}, {Ara*, 22}, {Aries, 5596}, {Auriga (1st)*, 5601}, {Auriga (2nd)*, 5602}, {Brocard (1st)\$-, 2896}, {Brocard (3rd), 194}, {Brocard (4th), 2}, {circummedial, 2}, {circumorthic, 6193}, {Euler*, 3091}, {Euler (5th), 2}, {extouch, 144}, {Fuhrmann, 8}, {Garcia (inner)\$-, 3648}, {Garcia (outer)*, 8}, {Grebe (inner)*, 1271}, {Grebe (outer)*, 1270}, {Honsberger, 7674}, {incentral, 192}, {intouch, 145}, {Johnson*, 4}, {Lemoine, 1992}, {Lucas homothetic*, 6462}, {Lucas(-1) homothetic*, 6463}, {Macbeath, 4}, {McCay, 7616}, {medial*, 2}, {mixtilinear (5th)*, 145}, {Napoleon (inner), 627}, {Napoleon (outer), 628}, {Neuberg (1st), 6194}, {Neuberg (2nd), 147}, {orthic, 193}, {Steiner, 0}, {symmedial, 194}, {Vecten (inner), 488}, {Vecten (outer), 487}, {Yff contact, 512} Antlia {Aquila, 1}, {circumperp (2nd), 1}, {excentral, 1}, {incentral, 1}, {intouch, 5575}, {medial, 5574}, {midarc, 1}, {mixtilinear, 1}, {mixtilinear (2nd), 1}, {mixtilinear (5th), 1} Apus {excentral, 3}, {extangents, 5584}, {Feuerbach, 4}, {hexyl, 3}, {incentral, 56}, {mixtilinear (2nd), 8273}, {mixtilinear (4th), 55}, {tangential, 198} Aquila {Ara*, 8185}, {Auriga (1st)*, 8186}, {Auriga (2nd)*, 8187}, {circumperp (2nd), 1}, {Euler*, 1699}, {excentral, 1}, {extangents, 8274}, {Garcia (inner)\$-, 3632}, {Garcia (outer)*, 3679}, {Grebe (inner)*, 5589}, {Grebe (outer)*, 5588}, {hexyl, 1768}, {Hutson (intouch), 8275}, {incentral, 1}, {intouch, 5586}, {Johnson*, 5587}, {Lucas homothetic*, 8188}, {Lucas(-1) homothetic*, 8189}, {medial*, 1698}, {midarc, 1}, {mixtilinear, 1}, {mixtilinear (2nd), 1}, {mixtilinear (5th)*, 1}, {mixtilinear (6th), 7992} Ara {Aries, 7387}, {Auriga (1st)*, 8190}, {Auriga (2nd)*, 8191}, {Brocard (1st)\$-, 3}, {circumperp (1st), 3}, {circumperp (2nd), 3}, {Euler*, 1598}, {Euler (2nd), 3}, {Fuhrmann, 3}, {Garcia (outer)*, 8193}, {Grebe (inner)*, 5595}, {Grebe (outer)*, 5594}, {Johnson*, 3}, {Lucas central, 8276}, {Lucas homothetic*, 8194}, {Lucas(-1) central, 8277}, {Lucas(-1) homothetic*, 8195}, {McCay, 3}, {medial*, 3}, {mixtilinear (3rd), 8278}, {mixtilinear (5th)*, 8192}, {Napoleon (inner), 3}, {Napoleon (outer), 3}, {Neuberg (1st), 3}, {Neuberg (2nd), 3}, {tangential, 3}, {Trinh, 3}, {Vecten (inner), 3}, {Vecten (outer), 3} Aries {Lucas antipodal, 1151}, {Lucas(-1) antipodal, 1152}, {Steiner, 1632}, {tangential, 1498} Auriga (1st) {Auriga (2nd)*, 55}, {Euler*, 8196}, {Garcia (outer)*, 8197}, {Grebe (inner)*, 8198}, {Grebe (outer)*, 8199}, {Johnson*, 8200}, {Lucas homothetic*, 8201}, {Lucas(-1) homothetic*, 8202}, {medial*, 5599}, {mixtilinear (5th)*, 5598} Auriga (2nd) {Euler*, 8203}, {Garcia (outer)*, 8204}, {Grebe (inner)*, 8205}, {Grebe (outer)*, 8206}, {Johnson*, 8207}, {Lucas homothetic*, 8208}, {Lucas(-1) homothetic*, 8209}, {medial*, 5600}, {mixtilinear (5th)*, 5597} bci {excentral, 3645}, {tangential-midarc, 1}, {tangential-midarc (2nd), 1} Brocard (1st) {Brocard (2nd), 2}, {Brocard (3rd), 384}, {circumperp (1st), 3}, {circumperp (2nd), 3}, {Euler (2nd), 3}, {excentral, 3496}, {Fuhrmann, 3}, {Johnson\$-, 3}, {McCay, 3}, {medial\$-, 3}, {Napoleon (inner), 3}, {Napoleon (outer), 3}, {Neuberg (1st), 3}, {Neuberg (2nd), 3}, {tangential, 3}, {Trinh, 3}, {Vecten (inner), 3}, {Vecten (outer), 3} Brocard (2nd) {circumsymmedial, 6}, {Grebe (inner), 6}, {Grebe (outer), 6}, {Lucas Brocard, 0}, {Lucas(-1) Brocard, 0}, {symmedial, 6}, {tangential, 6} Brocard (3rd) {circumsymmedial, 6195}, {excentral, 6196}, {Neuberg (1st), 4}, {symmedial, 194}, {tangential, 3499} Brocard (4th) {circummedial, 2}, {Euler (5th), 2}, {medial, 2}, {Napoleon (inner), 16}, {Napoleon (outer), 15}, {orthocentroidal, 6} circummedial {Euler (5th)*, 2}, {Macbeath, 25}, {medial, 2}, {tangential, 22} circumorthic {Euler, 4}, {Euler (2nd)*, 2}, {extangents*, 6197}, {extouch (2nd), 4}, {extouch (3rd), 4}, {intangents*, 6198}, {Johnson, 110}, {Macbeath, 3}, {midheight, 4}, {orthic*, 4}, {orthocentroidal, 4}, {reflection, 4}, {tangential*, 24}, {Trinh*, 3520} circumperp (1st) {circumperp (2nd)*, 3}, {Euler (2nd), 3}, {Euler (3rd)*, 2}, {Euler (4th)*, 4}, {excentral*, 165}, {extouch (2nd)*, 7580}, {Fuhrmann\$-, 3}, {hexyl*, 40}, {Honsberger*, 7676}, {Hutson (inner)*, 8107}, {Hutson (intouch)*, 56}, {Hutson (outer)*, 8108}, {intouch*, 55}, {Johnson, 3}, {McCay, 3}, {medial, 3}, {mixtilinear (3rd), 1}, {mixtilinear (4th), 165}, {mixtilinear (6th)*, 165}, {Napoleon (inner), 3}, {Napoleon (outer), 3}, {Neuberg (1st), 3}, {Neuberg (2nd), 3}, {Pamfilos-Zhou (1st), 0}, {Pamfilos-Zhou (2nd)*, 8224}, {Sharygin (1st)*, 4220}, {Sharygin (2nd)\$, 105}, {tangential, 3}, {tangential-midarc*, 8075}, {tangential-midarc (2nd)*, 8076}, {Trinh, 3}, {Vecten (inner), 3}, {Vecten (outer), 3}, {Yff central*, 7589}, {Yff contact, 100} circumperp (2nd) {Euler (2nd), 3}, {Euler (3rd)*, 4}, {Euler (4th)*, 2}, {excentral*, 1}, {extouch (2nd)*, 405}, {extouch (5th), 8283}, {Fuhrmann\$-, 3}, {Garcia (outer), 100}, {hexyl*, 3576}, {Honsberger*, 7677}, {Hutson (inner)*, 8109}, {Hutson (intouch)*, 55}, {Hutson (outer)*, 8110}, {incentral, 1}, {intouch*, 56}, {Johnson, 3}, {McCay, 3}, {medial, 3}, {midarc, 1}, {mixtilinear, 1}, {mixtilinear (2nd), 1}, {mixtilinear (5th), 1}, {mixtilinear (6th)*, 7987}, {Napoleon (inner), 3}, {Napoleon (outer), 3}, {Neuberg (1st), 3}, {Neuberg (2nd), 3}, {Pamfilos-Zhou (1st), 0}, {Pamfilos-Zhou (2nd)*, 8225}, {Sharygin (1st)*, 21}, {Sharygin (2nd)\$, 100}, {tangential, 3}, {tangential-midarc*, 8077}, {tangential-midarc (2nd)*, 7588}, {Trinh, 3}, {Vecten (inner), 3}, {Vecten (outer), 3}, {Yff central*, 7587} circumsymmedial {Grebe (inner), 6}, {Grebe (outer), 6}, {Lucas Brocard, 0}, {Lucas central, 6199}, {Lucas inner, 6221}, {Lucas inner tangential, 6433}, {Lucas reflection, 0}, {Lucas secondary central, 3}, {Lucas secondary tangents (1st), 6396}, {Lucas secondary tangents (2nd), 6435}, {Lucas tangents, 6200}, {Lucas(-1) Brocard, 0}, {Lucas(-1) central, 6395}, {Lucas(-1) inner, 6398}, {Lucas(-1) inner tangential, 6434}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 3}, {Lucas(-1) secondary tangents (1st), 6200}, {Lucas(-1) secondary tangents (2nd), 6436}, {Lucas(-1) tangents, 6396}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8296}, {Sharygin (2nd), 8297}, {symmedial, 6}, {tangential, 6} Euler {Euler (3rd), 946}, {extouch (2nd), 4}, {extouch (3rd), 4}, {Garcia (outer)*, 5587}, {Grebe (inner)*, 6202}, {Grebe (outer)*, 6201}, {Johnson*, 381}, {Lucas homothetic*, 8212}, {Lucas(-1) homothetic*, 8213}, {medial*, 5}, {midheight, 4}, {mixtilinear (5th)*, 5603}, {orthic, 4}, {orthocentroidal\$-, 4}, {reflection, 4} Euler (2nd) {extangents*, 8251}, {Fuhrmann, 3}, {Garcia (inner), 8279}, {intangents*, 1062}, {Johnson, 3}, {McCay, 3}, {medial, 3}, {Napoleon (inner), 3}, {Napoleon (outer), 3}, {Neuberg (1st), 3}, {Neuberg (2nd), 3}, {orthic*, 5}, {tangential*, 3}, {Trinh*, 3}, {Vecten (inner), 3}, {Vecten (outer), 3} Euler (3rd) {Euler (4th)*, 5}, {excentral*, 1699}, {extouch (2nd)*, 8226}, {hexyl*, 8227}, {Honsberger*, 7678}, {Hutson (inner)*, 0}, {Hutson (intouch)*, 12}, {Hutson (outer)*, 0}, {intouch*, 11}, {mixtilinear (6th)*, 7988}, {Pamfilos-Zhou (2nd)*, 8228}, {Sharygin (1st)*, 8229}, {tangential-midarc*, 8085}, {tangential-midarc (2nd)*, 8086}, {Yff central*, 0} Euler (4th) {excentral*, 1698}, {extouch (2nd)*, 442}, {Feuerbach, 442}, {hexyl*, 5587}, {Honsberger*, 7679}, {Hutson (extouch), 442}, {Hutson (inner)*, 0}, {Hutson (intouch)*, 11}, {Hutson (outer)*, 0}, {intouch*, 12}, {medial, 10}, {mixtilinear (6th)*, 7989}, {Pamfilos-Zhou (2nd)*, 8230}, {Sharygin (1st)*, 5051}, {tangential-midarc*, 8087}, {tangential-midarc (2nd)*, 8088}, {Yff central*, 0} Euler (5th) {medial, 2}, {orthic, 427}, {squares (inner), 8280}, {squares (outer), 8281} excentral {extangents, 40}, {extouch, 40}, {extouch (2nd)*, 9}, {extouch (3rd), 3182}, {Feuerbach, 5}, {Fuhrmann\$-, 191}, {Garcia (inner), 40}, {Garcia (outer), 40}, {hexyl*, 3}, {Honsberger*, 1445}, {Hutson (extouch), 40}, {Hutson (inner)*, 363}, {Hutson (intouch)*, 1697}, {Hutson (outer)*, 168}, {incentral, 1}, {intouch*, 57}, {Lemoine, 6205}, {Macbeath, 1726}, {McCay, 7609}, {medial, 9}, {midarc, 1}, {midheight, 57}, {mixtilinear, 1}, {mixtilinear (2nd), 1}, {mixtilinear (3rd), 7963}, {mixtilinear (4th), 165}, {mixtilinear (5th), 1}, {mixtilinear (6th)*, 165}, {Morley (1st), 1507}, {Morley (2nd), 6208}, {Morley (3rd), 6209}, {Morley adjunct (1st), 1508}, {Morley adjunct (2nd), 6206}, {Morley adjunct (3rd), 6207}, {Napoleon (inner), 6192}, {Napoleon (outer), 6191}, {Neuberg (1st), 6210}, {Neuberg (2nd), 6211}, {orthic, 46}, {orthocentroidal, 3336}, {Pamfilos-Zhou (1st), 0}, {Pamfilos-Zhou (2nd)*, 8231}, {reflection, 484}, {Sharygin (1st)*, 846}, {Sharygin (2nd)\$, 1282}, {squares (inner), 6204}, {squares (outer), 6203}, {Steiner, 1019}, {symmedial, 43}, {tangential-midarc*, 8078}, {tangential-midarc (2nd)*, 258}, {Vecten (inner), 6213}, {Vecten (outer), 6212}, {Yff central*, 173}, {Yff contact, 649} extangents {extouch, 40}, {Feuerbach, 3925}, {Garcia (inner), 40}, {Garcia (outer), 40}, {Hutson (extouch), 40}, {incentral, 55}, {intangents*, 55}, {mixtilinear (2nd), 7957}, {mixtilinear (4th), 7964}, {orthic*, 19}, {tangential*, 55}, {Trinh*, 7688} extouch {extouch (2nd), 72}, {extouch (3rd), 5930}, {extouch (5th), 5930}, {Garcia (inner), 40}, {Garcia (outer), 40}, {Hutson (extouch), 40}, {Hutson (intouch), 8}, {intangents, 200}, {midheight, 1}, {Schroeter, 8286}, {tangential, 197} extouch (2nd) {extouch (3rd), 4}, {extouch (4th), 5928}, {Feuerbach, 442}, {hexyl*, 1490}, {Honsberger*, 8232}, {Hutson (extouch), 442}, {Hutson (inner)*, 5934}, {Hutson (intouch)*, 950}, {Hutson (outer)*, 5935}, {intouch*, 226}, {medial, 9}, {midheight, 4}, {mixtilinear (6th)*, 1750}, {orthic, 4}, {orthocentroidal, 4}, {Pamfilos-Zhou (2nd)*, 8233}, {reflection, 4}, {Sharygin (1st)*, 4199}, {tangential-midarc*, 8079}, {tangential-midarc (2nd)*, 8080}, {Yff central*, 7593} extouch (3rd) {extouch (4th), 5929}, {extouch (5th), 5930}, {Garcia (outer), 8282}, {intouch, 1439}, {medial, 223}, {midheight, 4}, {orthic, 4}, {orthocentroidal, 4}, {reflection, 4}, {Soddy (inner), 0}, {Soddy (outer), 0} extouch (4th) {extouch (5th), 65}, {intouch, 65}, {Soddy (inner), 0}, {Soddy (outer), 0} extouch (5th) {intouch, 65}, {Soddy (inner), 0}, {Soddy (outer), 0} Feuerbach {Hutson (extouch), 442}, {incentral\$, 11}, {mixtilinear (2nd), 7958}, {mixtilinear (4th), 7965}, {Schroeter, 11} Fuhrmann {Garcia (outer), 8}, {Johnson, 3}, {McCay, 3}, {medial, 3}, {Napoleon (inner), 3}, {Napoleon (outer), 3}, {Neuberg (1st), 3}, {Neuberg (2nd), 3}, {tangential, 3}, {Trinh, 3}, {Vecten (inner), 3}, {Vecten (outer), 3} Garcia (inner) {Garcia (outer)\$-, 40}, {Hutson (extouch), 40}, {tangential, 2915}, {Trinh, 8284} Garcia (outer) {Grebe (inner)*, 5689}, {Grebe (outer)*, 5688}, {Hutson (extouch), 40}, {Johnson*, 517}, {Lucas homothetic*, 8214}, {Lucas(-1) homothetic*, 8215}, {medial*, 1}, {mixtilinear (5th)*, 519}, {Sharygin (2nd), 100} Grebe (inner) {Grebe (outer)*, 6}, {Johnson*, 6215}, {Lucas antipodal, 0}, {Lucas homothetic*, 8216}, {Lucas(-1) homothetic*, 8217}, {Lucas(-1) tangents, 6397}, {medial*, 5591}, {midheight, 6218}, {mixtilinear (5th)*, 5605}, {orthic, 1163}, {orthocentroidal\$-, 7720}, {reflection, 6220}, {symmedial, 6}, {tangential, 6} Grebe (outer) {Johnson*, 6214}, {Lucas homothetic*, 8218}, {Lucas tangents, 6216}, {Lucas(-1) antipodal, 0}, {Lucas(-1) homothetic*, 8219}, {medial*, 5590}, {midheight, 6217}, {mixtilinear (5th)*, 5604}, {orthic, 1162}, {orthocentroidal\$-, 7721}, {reflection, 6219}, {symmedial, 6}, {tangential, 6} hexyl {Honsberger*, 7675}, {Hutson (inner)*, 8111}, {Hutson (intouch)*, 1}, {Hutson (outer)*, 8112}, {intangents, 1}, {intouch*, 1}, {mixtilinear (5th), 7966}, {mixtilinear (6th)*, 1}, {Pamfilos-Zhou (2nd)*, 8234}, {Sharygin (1st)*, 8235}, {tangential-midarc*, 8081}, {tangential-midarc (2nd)*, 8082}, {Yff central*, 7590} Honsberger {Hutson (extouch), 7}, {Hutson (inner)*, 0}, {Hutson (intouch)*, 8236}, {Hutson (outer)*, 0}, {intouch*, 7}, {mixtilinear (6th)*, 4326}, {Pamfilos-Zhou (2nd)*, 8237}, {Sharygin (1st)*, 8238}, {tangential-midarc*, 0}, {tangential-midarc (2nd)*, 0}, {Yff central*, 0} Hutson (extouch) {intouch, 7} Hutson (inner) {Hutson (intouch)*, 0}, {Hutson (outer)*, 8140}, {intouch*, 8113}, {mixtilinear (6th)*, 8140}, {Pamfilos-Zhou (2nd)*, 0}, {Sharygin (1st)*, 0}, {tangential-midarc*, 8133}, {tangential-midarc (2nd)*, 6732}, {Yff central*, 0} Hutson (intouch) {Hutson (outer)*, 0}, {intangents, 1}, {intouch*, 1}, {mixtilinear (5th), 390}, {mixtilinear (6th)*, 1}, {Pamfilos-Zhou (2nd)*, 8239}, {Sharygin (1st)*, 8240}, {tangential-midarc*, 8241}, {tangential-midarc (2nd)*, 8242}, {Yff central*, 0} Hutson (outer) {intouch*, 8114}, {mixtilinear (6th)*, 8140}, {Pamfilos-Zhou (2nd)*, 0}, {Sharygin (1st)*, 0}, {tangential-midarc*, 8135}, {tangential-midarc (2nd)*, 8138}, {Yff central*, 7707} incentral {intangents, 55}, {Lucas homothetic, 0}, {Lucas(-1) homothetic, 0}, {midarc, 1}, {mixtilinear, 1}, {mixtilinear (2nd), 1}, {mixtilinear (4th), 57}, {mixtilinear (5th), 1}, {Schroeter, 11}, {Sharygin (2nd), 8298}, {tangential, 55} intangents {intouch, 1}, {mixtilinear (5th), 3057}, {mixtilinear (6th), 1}, {orthic*, 33}, {tangential*, 55}, {Trinh*, 36} intouch {midarc, 177}, {midheight, 57}, {mixtilinear (5th), 145}, {mixtilinear (6th)*, 1}, {Pamfilos-Zhou (2nd)*, 8243}, {Schroeter, 8287}, {Sharygin (1st)*, 1284}, {Soddy (inner), 482}, {Soddy (outer), 481}, {tangential, 1486}, {tangential-midarc*, 2089}, {tangential-midarc (2nd)*, 174}, {Yff central*, 174} Johnson {Lucas homothetic*, 8220}, {Lucas(-1) homothetic*, 8221}, {Macbeath, 4}, {McCay, 3}, {medial*, 3}, {mixtilinear (5th)*, 952}, {Napoleon (inner), 3}, {Napoleon (outer), 3}, {Neuberg (1st), 3}, {Neuberg (2nd), 3}, {orthic, 155}, {tangential, 3}, {Trinh, 3}, {Vecten (inner), 3}, {Vecten (outer), 3}, {Yiu, 5} Lemoine {Schroeter, 8288}, {tangential, 1995} Lucas antipodal {Lucas central, 3}, {Lucas homothetic, 6465}, {Lucas tangents, 6457}, {Lucas(-1) antipodal, 3}, {Lucas(-1) central, 3}, {squares (outer), 0}, {Vecten (inner), 6561} Lucas Brocard {Lucas central, 0}, {Lucas inner, 0}, {Lucas inner tangential, 1151}, {Lucas reflection, 0}, {Lucas secondary central, 0}, {Lucas secondary tangents (1st), 1151}, {Lucas secondary tangents (2nd), 0}, {Lucas tangents, 1151}, {Lucas(-1) Brocard, 574}, {Lucas(-1) central, 0}, {Lucas(-1) inner, 0}, {Lucas(-1) inner tangential, 0}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 0}, {Lucas(-1) secondary tangents (1st), 0}, {Lucas(-1) secondary tangents (2nd), 0}, {Lucas(-1) tangents, 0}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8318}, {Sharygin (2nd), 8334}, {symmedial, 5058}, {tangential, 1151} Lucas central {Lucas inner, 6407}, {Lucas inner tangential, 6453}, {Lucas reflection, 0}, {Lucas secondary central, 371}, {Lucas secondary tangents (1st), 6447}, {Lucas secondary tangents (2nd), 6449}, {Lucas tangents, 6221}, {Lucas(-1) antipodal, 3}, {Lucas(-1) Brocard, 0}, {Lucas(-1) central, 3}, {Lucas(-1) inner, 6446}, {Lucas(-1) inner tangential, 372}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 3311}, {Lucas(-1) secondary tangents (1st), 3311}, {Lucas(-1) secondary tangents (2nd), 6451}, {Lucas(-1) tangents, 3312}, {Neuberg (1st), 6222}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8320}, {Sharygin (2nd), 8336}, {symmedial, 3311}, {tangential, 371} Lucas homothetic {Lucas tangents, 0}, {Lucas(-1) homothetic*, 6461}, {medial*, 8222}, {mixtilinear (5th)*, 8210}, {symmedial, 6461} Lucas inner {Lucas inner tangential, 6468}, {Lucas reflection, 0}, {Lucas secondary central, 6472}, {Lucas secondary tangents (1st), 6476}, {Lucas secondary tangents (2nd), 6480}, {Lucas tangents, 6453}, {Lucas(-1) Brocard, 0}, {Lucas(-1) central, 6445}, {Lucas(-1) inner, 3}, {Lucas(-1) inner tangential, 6470}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 6474}, {Lucas(-1) secondary tangents (1st), 6478}, {Lucas(-1) secondary tangents (2nd), 6482}, {Lucas(-1) tangents, 371}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8322}, {Sharygin (2nd), 8338}, {symmedial, 6425}, {tangential, 6429} Lucas inner tangential {Lucas reflection, 0}, {Lucas secondary central, 6484}, {Lucas secondary tangents (1st), 1151}, {Lucas secondary tangents (2nd), 6490}, {Lucas tangents, 1151}, {Lucas(-1) Brocard, 0}, {Lucas(-1) central, 371}, {Lucas(-1) inner, 6471}, {Lucas(-1) inner tangential, 3}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 6486}, {Lucas(-1) secondary tangents (1st), 6488}, {Lucas(-1) secondary tangents (2nd), 6492}, {Lucas(-1) tangents, 6411}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8324}, {Sharygin (2nd), 8340}, {symmedial, 6409}, {tangential, 1151} Lucas reflection {Lucas secondary central, 0}, {Lucas secondary tangents (1st), 0}, {Lucas secondary tangents (2nd), 0}, {Lucas tangents, 0}, {Lucas(-1) Brocard, 0}, {Lucas(-1) central, 0}, {Lucas(-1) inner, 0}, {Lucas(-1) inner tangential, 0}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 0}, {Lucas(-1) secondary tangents (1st), 0}, {Lucas(-1) secondary tangents (2nd), 0}, {Lucas(-1) tangents, 0}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 0}, {Sharygin (2nd), 0}, {symmedial, 0}, {tangential, 0} Lucas secondary central {Lucas secondary tangents (1st), 3312}, {Lucas secondary tangents (2nd), 6494}, {Lucas tangents, 6449}, {Lucas(-1) Brocard, 0}, {Lucas(-1) central, 3312}, {Lucas(-1) inner, 6475}, {Lucas(-1) inner tangential, 6487}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 3}, {Lucas(-1) secondary tangents (1st), 6496}, {Lucas(-1) secondary tangents (2nd), 6498}, {Lucas(-1) tangents, 6456}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8326}, {Sharygin (2nd), 8342}, {symmedial, 3312}, {tangential, 371} Lucas secondary tangents (1st) {Lucas secondary tangents (2nd), 6199}, {Lucas tangents, 1151}, {Lucas(-1) Brocard, 0}, {Lucas(-1) central, 3312}, {Lucas(-1) inner, 6479}, {Lucas(-1) inner tangential, 6489}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 6497}, {Lucas(-1) secondary tangents (1st), 3}, {Lucas(-1) secondary tangents (2nd), 6500}, {Lucas(-1) tangents, 6396}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8328}, {Sharygin (2nd), 8344}, {symmedial, 3312}, {tangential, 1151} Lucas secondary tangents (2nd) {Lucas tangents, 6425}, {Lucas(-1) Brocard, 0}, {Lucas(-1) central, 6452}, {Lucas(-1) inner, 6483}, {Lucas(-1) inner tangential, 6493}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 6499}, {Lucas(-1) secondary tangents (1st), 6501}, {Lucas(-1) secondary tangents (2nd), 3}, {Lucas(-1) tangents, 372}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8330}, {Sharygin (2nd), 8346}, {symmedial, 6427}, {tangential, 6431} Lucas tangents {Lucas(-1) Brocard, 0}, {Lucas(-1) central, 3311}, {Lucas(-1) inner, 372}, {Lucas(-1) inner tangential, 6412}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 6455}, {Lucas(-1) secondary tangents (1st), 6200}, {Lucas(-1) secondary tangents (2nd), 371}, {Lucas(-1) tangents, 3}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8332}, {Sharygin (2nd), 8348}, {symmedial, 3}, {tangential, 1151} Lucas(-1) antipodal {Lucas(-1) central, 3}, {Lucas(-1) homothetic, 6466}, {Lucas(-1) tangents, 6458}, {squares (inner), 0}, {Vecten (outer), 6560} Lucas(-1) Brocard {Lucas(-1) central, 0}, {Lucas(-1) inner, 0}, {Lucas(-1) inner tangential, 1152}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 0}, {Lucas(-1) secondary tangents (1st), 1152}, {Lucas(-1) secondary tangents (2nd), 0}, {Lucas(-1) tangents, 1152}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8319}, {Sharygin (2nd), 8335}, {symmedial, 5062}, {tangential, 1152} Lucas(-1) central {Lucas(-1) inner, 6408}, {Lucas(-1) inner tangential, 6454}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 372}, {Lucas(-1) secondary tangents (1st), 6448}, {Lucas(-1) secondary tangents (2nd), 6450}, {Lucas(-1) tangents, 6398}, {Neuberg (1st), 6399}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8321}, {Sharygin (2nd), 8337}, {symmedial, 3312}, {tangential, 372} Lucas(-1) homothetic {Lucas(-1) tangents, 0}, {medial*, 8223}, {mixtilinear (5th)*, 8211}, {symmedial, 6461} Lucas(-1) inner {Lucas(-1) inner tangential, 6469}, {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 6473}, {Lucas(-1) secondary tangents (1st), 6477}, {Lucas(-1) secondary tangents (2nd), 6481}, {Lucas(-1) tangents, 6454}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8323}, {Sharygin (2nd), 8339}, {symmedial, 6426}, {tangential, 6430} Lucas(-1) inner tangential {Lucas(-1) reflection, 0}, {Lucas(-1) secondary central, 6485}, {Lucas(-1) secondary tangents (1st), 1152}, {Lucas(-1) secondary tangents (2nd), 6491}, {Lucas(-1) tangents, 1152}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8325}, {Sharygin (2nd), 8341}, {symmedial, 6410}, {tangential, 1152} Lucas(-1) reflection {Lucas(-1) secondary central, 0}, {Lucas(-1) secondary tangents (1st), 0}, {Lucas(-1) secondary tangents (2nd), 0}, {Lucas(-1) tangents, 0}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 0}, {Sharygin (2nd), 0}, {symmedial, 0}, {tangential, 0} Lucas(-1) secondary central {Lucas(-1) secondary tangents (1st), 3311}, {Lucas(-1) secondary tangents (2nd), 6495}, {Lucas(-1) tangents, 6450}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8327}, {Sharygin (2nd), 8343}, {symmedial, 3311}, {tangential, 372} Lucas(-1) secondary tangents (1st) {Lucas(-1) secondary tangents (2nd), 6395}, {Lucas(-1) tangents, 1152}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8329}, {Sharygin (2nd), 8345}, {symmedial, 3311}, {tangential, 1152} Lucas(-1) secondary tangents (2nd) {Lucas(-1) tangents, 6426}, {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8331}, {Sharygin (2nd), 8347}, {symmedial, 6428}, {tangential, 6432} Lucas(-1) tangents {Pamfilos-Zhou (1st), 0}, {Sharygin (1st), 8333}, {Sharygin (2nd), 8349}, {symmedial, 3}, {tangential, 1152} Macbeath {Schroeter, 338}, {tangential, 157} McCay {medial, 3}, {Napoleon (inner), 3}, {Napoleon (outer), 3}, {Neuberg (1st), 3}, {Neuberg (2nd), 3}, {tangential, 3}, {Trinh, 3}, {Vecten (inner), 3}, {Vecten (outer), 3} medial {midarc, 178}, {midheight, 6}, {mixtilinear (5th)*, 8}, {Napoleon (inner), 3}, {Napoleon (outer), 3}, {Neuberg (1st), 3}, {Neuberg (2nd), 3}, {Schroeter, 115}, {Sharygin (2nd), 8299}, {squares (inner), 6}, {squares (outer), 6}, {tangential, 3}, {Trinh, 3}, {Vecten (inner), 3}, {Vecten (outer), 3} midarc {mixtilinear, 1}, {mixtilinear (2nd), 1}, {mixtilinear (5th), 1}, {tangential-midarc, 8083}, {tangential-midarc (2nd), 8084} midheight {orthic, 4}, {orthocentroidal, 4}, {reflection, 4}, {squares (inner), 6}, {squares (outer), 6} mixtilinear {mixtilinear (2nd)*, 1}, {mixtilinear (3rd), 3}, {mixtilinear (5th), 1}, {Sharygin (1st), 0} mixtilinear (2nd) {mixtilinear (4th), 3}, {mixtilinear (5th), 1}, {Sharygin (2nd), 8285} mixtilinear (3rd) {mixtilinear (5th), 100}, {tangential, 1616} mixtilinear (4th) {mixtilinear (6th), 165}, {tangential, 1615} mixtilinear (5th) {mixtilinear (6th), 7990}, {tangential-midarc (2nd), 0} mixtilinear (6th) {Pamfilos-Zhou (2nd)*, 8244}, {Sharygin (1st)*, 8245}, {tangential-midarc*, 8089}, {tangential-midarc (2nd)*, 8090}, {Yff central*, 0} Morley (1st) {Morley (2nd)*, 358}, {Morley (3rd)*, 1135}, {Morley adjunct (1st), 356}, {Stammler*, 8002} Morley (2nd) {Morley (3rd)*, 1137}, {Morley adjunct (2nd), 3276}, {Stammler*, 8003} Morley (3rd) {Morley adjunct (3rd), 3277}, {Stammler*, 8004} Napoleon (inner) {Napoleon (outer)\$-, 3}, {Neuberg (1st), 3}, {Neuberg (2nd), 3}, {orthocentroidal, 61}, {tangential, 3}, {Trinh, 3}, {Vecten (inner), 3}, {Vecten (outer), 3} Napoleon (outer) {Neuberg (1st), 3}, {Neuberg (2nd), 3}, {orthocentroidal, 62}, {tangential, 3}, {Trinh, 3}, {Vecten (inner), 3}, {Vecten (outer), 3} Neuberg (1st) {Neuberg (2nd), 3}, {tangential, 3}, {Trinh, 3}, {Vecten (inner), 3}, {Vecten (outer), 3} Neuberg (2nd) {tangential, 3}, {Trinh, 3}, {Vecten (inner), 3}, {Vecten (outer), 3} orthic {orthocentroidal, 4}, {reflection, 4}, {Schroeter, 125}, {squares (inner), 371}, {squares (outer), 372}, {tangential*, 25}, {Trinh*, 378}, {Vecten (inner), 371}, {Vecten (outer), 372} orthocentroidal {reflection, 4} Pamfilos-Zhou (1st) {Sharygin (1st), 0}, {Sharygin (2nd), 0}, {symmedial, 0}, {tangential, 0}, {Vecten (outer), 0} Pamfilos-Zhou (2nd) {Sharygin (1st)*, 8246}, {tangential-midarc*, 8247}, {tangential-midarc (2nd)*, 8248}, {Yff central*, 0} Schroeter {Steiner*, 2}, {symmedial, 7668}, {Yff contact, 1213} Sharygin (1st) {Sharygin (2nd)\$, 1281}, {symmedial, 1580}, {tangential, 0}, {tangential-midarc*, 8249}, {tangential-midarc (2nd)*, 8250}, {Yff central*, 0} Sharygin (2nd) {symmedial, 8300}, {tangential, 8301} Soddy (inner) {Soddy (outer), 1} squares (inner) {squares (outer), 6}, {Vecten (inner), 371}, {Vecten (outer), 485} squares (outer) {Vecten (inner), 486}, {Vecten (outer), 372} Steiner {tangential, 669} symmedial {tangential, 6} tangential {Trinh*, 3}, {Vecten (inner), 3}, {Vecten (outer), 3}, {Yff contact, 4057}, {Yiu, 195} tangential-midarc {tangential-midarc (2nd)*, 1}, {Yff central*, 177} tangential-midarc (2nd) {Yff central*, 174} Trinh {Vecten (inner), 3}, {Vecten (outer), 3} Vecten (inner) {Vecten (outer), 3}
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