The appearance of (T, T', n) in the following list means that the center of the common inconic of T and T' is X(n) (n=0 means a not calculated center): 


(ABC, ABC-X3 reflections, 3), (ABC, 1st anti-circumperp, 512), (ABC, anti-Honsberger, 3589), (ABC, anti-tangential-midarc, 1), (ABC, anti-Ursa minor, 3589), (ABC, anti-Wasat, 389), (ABC, Aries, 65386), (ABC, 9th Brocard, 13567), (ABC, circummedial, 3934), (ABC, circumnormal, 140), (ABC, circumorthic, 389), (ABC, 1st circumperp, 514), (ABC, 2nd circumperp, 1125), (ABC, circumsymmedial, 39), (ABC, circumtangential, 523), (ABC, inner-Conway, 513), (ABC, outer-Garcia, 10), (ABC, Garcia-reflection, 11019), (ABC, Gossard, 402), (ABC, Honsberger, 5572), (ABC, intangents, 1), (ABC, Johnson, 5), (ABC, 3rd mixtilinear, 52541), (ABC, 4th mixtilinear, 1212), (ABC, 5th mixtilinear, 1), (ABC, 1st Schiffler, 65387), (ABC, 2nd Schiffler, 65388), (ABC, tangential-midarc, 1), (ABC, 2nd tangential-midarc, 1), (ABC, Ursa-minor, 5572), (ABC, Wasat, 1125), 

(ABC-X3 reflections, 1st anti-circumperp, 15644), (ABC-X3 reflections, circummedial, 65389), (ABC-X3 reflections, circumnormal, 523), (ABC-X3 reflections, circumorthic, 512), (ABC-X3 reflections, 1st circumperp, 12512), (ABC-X3 reflections, 2nd circumperp, 514), (ABC-X3 reflections, circumsymmedial, 65390), (ABC-X3 reflections, circumtangential, 548), (ABC-X3 reflections, 3rd mixtilinear, 65391), (ABC-X3 reflections, 4th mixtilinear, 65392), 

(anti-Aquila, Ehrmann-mid, 9955), (anti-Aquila, incentral, 58380), (anti-Aquila, medial, 1125), 

(anti-Ara, 2nd anti-Conway, 523), (anti-Ara, 2nd Hyacinth, 65393), (anti-Ara, orthic axes, 65394), (anti-Ara, Pelletier, 65395), (anti-Ara, Schröeter, 65396), 

(1st anti-Auriga, 2nd anti-Auriga, 1), 

(2nd anti-circumperp-tangential, Hutson intouch, 514), (2nd anti-circumperp-tangential, intouch, 4298), (2nd anti-circumperp-tangential, Mandart-incircle, 1), (2nd anti-circumperp-tangential, midarc, 65397), (2nd anti-circumperp-tangential, 2nd midarc, 65398), 

(1st anti-circumperp, Aries, 924), (1st anti-circumperp, circummedial, 7750), (1st anti-circumperp, circumnormal, 10627), (1st anti-circumperp, circumorthic, 3), (1st anti-circumperp, 1st circumperp, 65424), (1st anti-circumperp, 2nd circumperp, 65399), (1st anti-circumperp, circumsymmedial, 65400), (1st anti-circumperp, circumtangential, 1510), (1st anti-circumperp, inner-Conway, 65401), (1st anti-circumperp, 3rd mixtilinear, 0), (1st anti-circumperp, 4th mixtilinear, 0), 

(2nd anti-Conway, 2nd Hyacinth, 3566), (2nd anti-Conway, midheight, 65402), (2nd anti-Conway, orthic axes, 65403), (2nd anti-Conway, Pelletier, 900), (2nd anti-Conway, Schröeter, 804), 

(anti-Ehrmann-mid, anti-Euler, 5), (anti-Ehrmann-mid, Aquila, 18480), (anti-Ehrmann-mid, X3-ABC reflections, 4), 

(anti-Euler, 4th anti-Euler, 185), (anti-Euler, anti-Hutson intouch, 44882), (anti-Euler, anticomplementary, 3), (anti-Euler, hexyl, 4297), 

(3rd anti-Euler, 4th anti-Euler, 3), (3rd anti-Euler, anticomplementary, 5562), (3rd anti-Euler, excentral, 31737), (3rd anti-Euler, Stammler, 6101), 

(4th anti-Euler, hexyl, 31732), 

(anti-excenters-reflections, orthic, 4), 

(anti-Honsberger, anti-Ursa minor, 3589), (anti-Honsberger, Ehrmann-vertex, 19130), (anti-Honsberger, 2nd Ehrmann, 6), (anti-Honsberger, Trinh, 5092), 

(anti-Hutson intouch, anti-Mandart-incircle, 3), (anti-Hutson intouch, 2nd circumperp tangential, 3), (anti-Hutson intouch, hexyl, 65404), (anti-Hutson intouch, Stammler, 3), (anti-Hutson intouch, tangential, 3), 

(anti-incircle-circles, anti-inverse-in-incircle, 5), (anti-incircle-circles, Ara, 6759), (anti-incircle-circles, 1st excosine, 6759), 

(anti-inverse-in-incircle, 2nd Conway, 1836), (anti-inverse-in-incircle, Steiner, 3566), (anti-inverse-in-incircle, Yff contact, 48269), 

(anti-Mandart-incircle, 2nd circumperp tangential, 3), (anti-Mandart-incircle, excentral, 65405), (anti-Mandart-incircle, Stammler, 3), (anti-Mandart-incircle, tangential, 3), 

(anti-McCay, 1st Parry, 542), 

(6th anti-mixtilinear, midheight, 65406), (6th anti-mixtilinear, Moses-Soddy, 65407), (6th anti-mixtilinear, Schröeter, 65408), (6th anti-mixtilinear, 1st Zaniah, 65409), (6th anti-mixtilinear, 2nd Zaniah, 65410), 

(1st anti-Parry, 2nd anti-Parry, 3), 

(anti-tangential-midarc, intangents, 1), (anti-tangential-midarc, 5th mixtilinear, 1), (anti-tangential-midarc, tangential-midarc, 1), (anti-tangential-midarc, 2nd tangential-midarc, 1), 

(anti-Ursa minor, Kosnita, 140), (anti-Ursa minor, Wasat, 3838), 

(anti-Wasat, circumorthic, 389), (anti-Wasat, Wasat, 31757), 

(anti-X3-ABC reflections, Ehrmann-mid, 5), (anti-X3-ABC reflections, medial, 140), 

(anti-inner-Yff, outer-Johnson, 5), 

(anti-outer-Yff, inner-Johnson, 5), 

(anticomplementary, Aquila, 10), (anticomplementary, Bevan antipodal, 3452), (anticomplementary, excentral, 10), (anticomplementary, Moses-Soddy, 514), (anticomplementary, Pelletier, 4885), (anticomplementary, Schröeter, 523), (anticomplementary, Soddy, 9), (anticomplementary, Stammler, 5), (anticomplementary, tangential, 141), (anticomplementary, X-parabola-tangential, 620), (anticomplementary, X3-ABC reflections, 5), 

(Aquila, excentral, 10), 

(Ara, 1st excosine, 6759), (Ara, Steiner, 525), 

(Aries, circumtangential, 0), 

(1st Auriga, 2nd Auriga, 55), 

(BCE-incenters, tangential-midarc, 65411), 

(Bevan antipodal, excentral, 3), (Bevan antipodal, hexyl, 3), (Bevan antipodal, Moses-Soddy, 65412), (Bevan antipodal, Pelletier, 65413), (Bevan antipodal, Schröeter, 65414), (Bevan antipodal, Soddy, 65415), (Bevan antipodal, tangential, 65416), (Bevan antipodal, X-parabola-tangential, 0), 

(1st Brocard, 2nd Brocard, 10007), (1st Brocard, 7th Brocard, 804), (1st Brocard, 10th Brocard, 0), (1st Brocard, 11th Brocard, 0), 

(2nd Brocard, 7th Brocard, 65417), (2nd Brocard, 10th Brocard, 0), (2nd Brocard, 11th Brocard, 0), 

(4th Brocard, orthocentroidal, 7753), 

(7th Brocard, 10th Brocard, 182), (7th Brocard, 11th Brocard, 0), 

(10th Brocard, 11th Brocard, 0), 

(circummedial, circumnormal, 65418), (circummedial, circumorthic, 65419), (circummedial, 1st circumperp, 0), (circummedial, 2nd circumperp, 0), (circummedial, circumsymmedial, 65420), (circummedial, circumtangential, 65421), (circummedial, 3rd mixtilinear, 0), (circummedial, 4th mixtilinear, 0), 

(circumnormal, circumorthic, 1510), (circumnormal, 1st circumperp, 31663), (circumnormal, 2nd circumperp, 513), (circumnormal, circumsymmedial, 65422), (circumnormal, circumtangential, 3), (circumnormal, Kosnita, 3), (circumnormal, 3rd mixtilinear, 0), (circumnormal, 4th mixtilinear, 0), (circumnormal, Trinh, 3), 

(circumorthic, 1st circumperp, 65423), (circumorthic, 2nd circumperp, 65424), (circumorthic, circumsymmedial, 65425), (circumorthic, circumtangential, 13630), (circumorthic, Ehrmann-side, 5), (circumorthic, 3rd mixtilinear, 0), (circumorthic, 4th mixtilinear, 0), 

(2nd circumperp tangential, hexyl, 65426), (2nd circumperp tangential, Stammler, 3), (2nd circumperp tangential, tangential, 3), 

(1st circumperp, 2nd circumperp, 3), (1st circumperp, circumsymmedial, 0), (1st circumperp, circumtangential, 513), (1st circumperp, 3rd mixtilinear, 0), (1st circumperp, 4th mixtilinear, 65427), 

(2nd circumperp, circumsymmedial, 0), (2nd circumperp, circumtangential, 13624), (2nd circumperp, 3rd mixtilinear, 65428), (2nd circumperp, 4th mixtilinear, 0), (2nd circumperp, Wasat, 1125), 

(circumsymmedial, circumtangential, 65429), (circumsymmedial, 2nd Ehrmann, 65430), (circumsymmedial, 3rd mixtilinear, 0), (circumsymmedial, 4th mixtilinear, 0), 

(circumtangential, Ehrmann-vertex, 125), (circumtangential, Kosnita, 3), (circumtangential, 3rd mixtilinear, 65431), (circumtangential, 4th mixtilinear, 0), (circumtangential, 1st Neuberg, 5092), (circumtangential, Trinh, 3), 

(inner-Conway, Honsberger, 9), 

(2nd Conway, Steiner, 4897), (2nd Conway, Yff contact, 3667), 

(Dao, extouch, 65432), (Dao, 2nd Hatzipolakis, 0), (Dao, incentral, 65503), (Dao, intouch, 65504), (Dao, Lemoine, 65505), (Dao, Macbeath, 65506), (Dao, medial, 65507), (Dao, orthic, 65508), (Dao, Steiner, 65509), (Dao, symmedial, 65510), (Dao, Yff contact, 65433), 

(Ehrmann-mid, Euler, 546), 

(Ehrmann-side, Johnson, 5907), 

(Ehrmann-vertex, Kosnita, 5), 

(2nd Ehrmann, Kosnita, 575), 

(Euler, 2nd Euler, 512), (Euler, 3rd Euler, 12571), (Euler, 4th Euler, 514), (Euler, 5th Euler, 65434), (Euler, Feuerbach, 0), (Euler, medial, 5), (Euler, orthic, 10110), 

(2nd Euler, 3rd Euler, 65435), (2nd Euler, 4th Euler, 65424), (2nd Euler, 5th Euler, 65436), (2nd Euler, Feuerbach, 0), (2nd Euler, medial, 11793), (2nd Euler, orthic, 5), 

(3rd Euler, 4th Euler, 5), (3rd Euler, 5th Euler, 0), (3rd Euler, Feuerbach, 65437), (3rd Euler, medial, 514), (3rd Euler, orthic, 65424), 

(4th Euler, 5th Euler, 0), (4th Euler, Feuerbach, 65438), (4th Euler, medial, 3634), (4th Euler, orthic, 58474), 

(5th Euler, Feuerbach, 0), (5th Euler, medial, 6683), (5th Euler, orthic, 7745), 

(excenters-midpoints, medial, 20103), 

(excenters-reflections, excentral, 1), 

(excentral, hexyl, 3), (excentral, Moses-Soddy, 3667), (excentral, Pelletier, 3309), (excentral, Schröeter, 14321), (excentral, Soddy, 10164), (excentral, Stammler, 3579), (excentral, tangential, 4640), (excentral, X-parabola-tangential, 65439), 

(1st excosine, Steiner, 65440), 

(2nd excosine, extangents, 65441), 

(extouch, 2nd Hatzipolakis, 0), (extouch, incentral, 65442), (extouch, intouch, 17115), (extouch, Lemoine, 65443), (extouch, Macbeath, 65444), (extouch, Mandart-incircle, 522), (extouch, medial, 3900), (extouch, orthic, 65445), (extouch, Steiner, 65446), (extouch, symmedial, 65447), (extouch, Yff contact, 65448), 

(11th Fermat-Dao, outer-Napoleon, 5), 

(12th Fermat-Dao, inner-Napoleon, 5), 

(1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 2), 

(3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 2), 

(1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 2), 

(3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2), 

(Feuerbach, Lemoine, 0), (Feuerbach, medial, 65449), (Feuerbach, orthic, 65450), 

(Garcia-reflection, 1st Schiffler, 65451), (Garcia-reflection, 2nd Schiffler, 11), (Garcia-reflection, Ursa-minor, 942), (Garcia-reflection, Wasat, 65452), 

(2nd Hatzipolakis, incentral, 0), (2nd Hatzipolakis, intouch, 0), (2nd Hatzipolakis, Lemoine, 0), (2nd Hatzipolakis, Macbeath, 0), (2nd Hatzipolakis, medial, 65511), (2nd Hatzipolakis, orthic, 0), (2nd Hatzipolakis, Steiner, 0), (2nd Hatzipolakis, symmedial, 0), (2nd Hatzipolakis, Yff contact, 0), 

(Honsberger, Ursa-minor, 5572), 

(Hutson intouch, intouch, 1), (Hutson intouch, Mandart-incircle, 12575), (Hutson intouch, midarc, 65453), (Hutson intouch, 2nd midarc, 65454), 

(2nd Hyacinth, orthic axes, 65455), (2nd Hyacinth, Pelletier, 65456), (2nd Hyacinth, Schröeter, 65457), 

(incentral, intouch, 2488), (incentral, Lemoine, 65458), (incentral, Macbeath, 65459), (incentral, Mandart-incircle, 523), (incentral, medial, 512), (incentral, orthic, 512), (incentral, Steiner, 5027), (incentral, symmedial, 669), (incentral, Yff contact, 890), 

(incircle-circles, inverse-in-incircle, 5045), (incircle-circles, 1st Savin, 65460), (incircle-circles, 2nd Zaniah, 1125), 

(intangents, 5th mixtilinear, 1), (intangents, tangential-midarc, 1), (intangents, 2nd tangential-midarc, 1), (intangents, Ursa-minor, 10391), 

(intouch, Lemoine, 65461), (intouch, Macbeath, 65462), (intouch, Mandart-incircle, 514), (intouch, medial, 513), (intouch, midarc, 58616), (intouch, 2nd midarc, 65453), (intouch, orthic, 2520), (intouch, Steiner, 65463), (intouch, symmedial, 65464), (intouch, Yff contact, 2976), 

(inverse-in-incircle, Moses-Soddy, 812), (inverse-in-incircle, Pelletier, 3887), (inverse-in-incircle, 1st Savin, 6002), (inverse-in-incircle, 1st Zaniah, 65465), 

(inner-Johnson, Ursa-major, 65466), 

(1st Johnson-Yff, inner-Yff, 495), 

(2nd Johnson-Yff, outer-Yff, 496), 

(Kosnita, Trinh, 3), 

(Lemoine, Macbeath, 65467), (Lemoine, medial, 12073), (Lemoine, orthic, 65468), (Lemoine, Steiner, 65469), (Lemoine, symmedial, 65470), (Lemoine, Yff contact, 65471), 

(Macbeath, medial, 6368), (Macbeath, orthic, 65472), (Macbeath, Steiner, 65473), (Macbeath, symmedial, 65474), (Macbeath, Yff contact, 65475), 

(Mandart-incircle, midarc, 65476), (Mandart-incircle, 2nd midarc, 65397), (Mandart-incircle, orthic, 513), 

(medial, orthic, 512), (medial, Steiner, 690), (medial, symmedial, 688), (medial, Yff contact, 900), 

(midarc, 2nd midarc, 1), 

(midheight, Moses-Soddy, 65477), (midheight, Schröeter, 65478), (midheight, 1st Zaniah, 65479), (midheight, 2nd Zaniah, 65480), 

(3rd mixtilinear, 4th mixtilinear, 65481), 

(5th mixtilinear, tangential-midarc, 1), (5th mixtilinear, 2nd tangential-midarc, 1), 

(6th mixtilinear, Yff contact, 15599), 

(Moses-Soddy, Pelletier, 17761), (Moses-Soddy, 1st Savin, 65482), (Moses-Soddy, Schröeter, 3120), (Moses-Soddy, Soddy, 59612), (Moses-Soddy, tangential, 3798), (Moses-Soddy, X-parabola-tangential, 21200), (Moses-Soddy, 1st Zaniah, 65483), (Moses-Soddy, 2nd Zaniah, 2505), 

(orthic, Steiner, 65484), (orthic, symmedial, 65485), (orthic, Yff contact, 65486), 

(orthic axes, Pelletier, 65487), (orthic axes, Schröeter, 65488), 

(1st orthosymmedial, 2nd orthosymmedial, 0), 

(1st Parry, 2nd Parry, 351), (1st Parry, 3rd Parry, 0), 

(2nd Parry, 3rd Parry, 65489), 

(1st Pavlov, 2nd Pavlov, 523), 

(Pelletier, 1st Savin, 65490), (Pelletier, Schröeter, 2486), (Pelletier, Soddy, 65491), (Pelletier, tangential, 15313), (Pelletier, X-parabola-tangential, 65492), 

(1st Schiffler, 2nd Schiffler, 65493), 

(Schröeter, Soddy, 65494), (Schröeter, tangential, 3566), (Schröeter, X-parabola-tangential, 10278), (Schröeter, 1st Zaniah, 65495), (Schröeter, 2nd Zaniah, 65496), 

(Soddy, tangential, 59607), (Soddy, X-parabola-tangential, 0), 

(Stammler, tangential, 3), (Stammler, X3-ABC reflections, 5), 

(Steiner, symmedial, 65497), (Steiner, Yff contact, 4427), 

(symmedial, Yff contact, 65498), 

(tangential, X-parabola-tangential, 5972), 

(tangential-midarc, 2nd tangential-midarc, 1), 

(1st Zaniah, 2nd Zaniah, 65499) 

=============================================================================================================

For certains pair of triangles, their common inconic is a parabola. The appearance of (T, T', n) in the following list means that the focus of the common inparabola (or common tangential parabola) of T and T' is X(n) (n=0 means a not calculated focus): 

(ABC, 1st anti-circumperp, 99), (ABC, 1st circumperp, 101), (ABC, circumtangential, 110), (ABC, inner-Conway, 100), (ABC-X3 reflections, circumnormal, 74), (ABC-X3 reflections, circumorthic, 98), (ABC-X3 reflections, 2nd circumperp, 103), (anti-Ara, 2nd anti-Conway, 1112), (2nd anti-circumperp-tangential, Hutson intouch, 1362), (2nd anti-circumperp-tangential, midarc, 0), (1st anti-circumperp, Aries, 925), (1st anti-circumperp, 1st circumperp, 65514), (1st anti-circumperp, circumtangential, 930), (2nd anti-Conway, 2nd Hyacinth, 65515), (2nd anti-Conway, orthic axes, 65500), (2nd anti-Conway, Pelletier, 65516), (2nd anti-Conway, Schröeter, 65517), (anti-inverse-in-incircle, Steiner, 65518), (anti-McCay, 1st Parry, 23), (anticomplementary, Moses-Soddy, 150), (anticomplementary, Schröeter, 3448), (Ara, Steiner, 11641), (BCE-incenters, tangential-midarc, 10215), (1st Brocard, 7th Brocard, 6), (circumnormal, circumorthic, 1141), (circumnormal, 2nd circumperp, 104), (circumorthic, 2nd circumperp, 65501), (1st circumperp, circumtangential, 100), (2nd Conway, Yff contact, 17777), (Dao, medial, 65513), (Euler, 2nd Euler, 114), (Euler, 4th Euler, 118), (2nd Euler, 4th Euler, 65519), (3rd Euler, medial, 116), (3rd Euler, orthic, 65520), (excentral, Moses-Soddy, 1054), (excentral, Pelletier, 5540), (extouch, Mandart-incircle, 1364), (extouch, medial, 5514), (2nd Hatzipolakis, medial, 65512), (Hutson intouch, midarc, 65502), (incentral, Mandart-incircle, 3024), (incentral, medial, 115), (incentral, orthic, 115), (intouch, Mandart-incircle, 3022), (intouch, medial, 11), (intouch, 2nd midarc, 10491), (inverse-in-incircle, Moses-Soddy, 65521), (inverse-in-incircle, Pelletier, 65522), (inverse-in-incircle, 1st Savin, 65523), (Lemoine, medial, 20389), (Macbeath, medial, 20625), (Mandart-incircle, 2nd midarc, 0), (Mandart-incircle, orthic, 11), (medial, orthic, 115), (medial, Steiner, 5099), (medial, symmedial, 35971), (medial, Yff contact, 3259), (1st Pavlov, 2nd Pavlov, 65524), (Pelletier, tangential, 14667), (Schröeter, tangential, 2079)

=============================================================================================================
César Lozada - Sept. 24, 2024.