X(10)    SPIEKER CENTER

The Spieker center, labeled 10, is 
X(1)-of-the-medial-triangle, A'B'C'.

Sketch contributed by Michael Stairs, 
January 2018.

Drag A, B, C.

10

2

A = (1.996841769917433, 4.188640544580252)
B = (-2.235596658324594, 0.3548742118079539)
f = Segment(A, B)
C = (3.1283855368664946, 0.4133029296192781)
g = Segment(B, C)
h = Segment(C, A)
C' = Midpoint(A, B)
A' = Midpoint(B, C)
B' = Midpoint(C, A)
i = Segment(C', A')
j = Segment(A', B')
k = Segment(B', C')
D = Incenter(C', A', B')
c = Incircle(C', A', B')
E = Centroid(A, C, B)
l = Segment(C, C')
m = Segment(B, B')
n = Segment(A, A')
p = Segment(C', D)
q = Segment(B', D)
r = Segment(A', D)

Tool: Centroid
Input: A, B, C
Output: G

D = Midpoint(A, B)
E = Midpoint(B, C)
s = Segment(C, D)
t = Segment(A, E)
G = Intersect(s, t)

Tool: Incenter
Input: A, B, C
Output: I

s = AngularBisector(B, A, C)
t = AngularBisector(A, B, C)
I = Intersect(s, t)

Tool: Incircle
Input: A, B, C
Output: c_1

g = Segment(A, C)
s = AngularBisector(B, A, C)
t = AngularBisector(A, B, C)
I = Intersect(s, t)
e = OrthogonalLine(I, g)
G = Intersect(e, g)
c_1 = Circle(I, G)