MathDB

The incircle of an acute-angled triangle

ABC

touches

AB, BC, CA

at points

C_1, A_1, B_1

respectively. Points

A_2, B_2

are the midpoints of the segments

B_1C_1, A_1C_1

respectively. Let

P

be a common point of the incircle and the line

CO

, where

O

is the circumcenter of triangle

ABC.

Let also

A'

and

B'

be the second common points of

PA_2

and

PB_2

with the incircle. Prove that a common point of

AA'

and

BB'

lies on the altitude of the triangle dropped from the vertex

C.

Problem Statement