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radius of circumcircle of T_AT_BT_C is twice the radius of circumcircle of ABC

Source: 2021 Turkey TST P7

May 23, 2021

number theoryChina second round

Problem Statement

Given a triangle

ABC

with the circumcircle

\omega

and incenter

I

. Let the line pass through the point

I

and the intersection of exterior angle bisector of

A

and

\omega

meets the circumcircle of

IBC

T_A

for the second time. Define

T_B

and

T_C

similarly. Prove that the radius of the circumcircle of the triangle

T_AT_BT_C

is twice the radius of

\omega