MathDB

I_a

is the excenter of the triangle

ABC

with respect to

A

, and

AI_a

intersects the circumcircle of

ABC

T

. Let

X

be a point on

TI_a

such that XI_a^2\equal{}XA.XT. Draw a perpendicular line from

X

BC

so that it intersects

BC

A'

. Define

B'

and

C'

in the same way. Prove that

AA'

BB'

and

CC'

are concurrent.

Problem Statement