Let AB and PQ be chords of circle Γ where AB is arbitrary and
PQ is the perpendicular bisector of AB. Let C be a point on Γ
distinct from points A and B. Let I be the incenter of ΔABC. Let
H be the intersection of the perpendicular bisectors of line segments
IA and IB.

Prove that H is either the point P or the point Q.
  

(In reply to Solution by Jer)

Don't you mean H (the circumcenter of triangle) AIB lies on the ray CI which passes through the excenter of triangle ABC opposite vertex C?

Edited on January 16, 2018, 11:18 am

Posted by Bractals on 2018-01-16 01:24:36