4

Part of 2017 BMO TST

Problems(1)

Albania BMO TST Problem 4

Source:

The incircle of

\triangle A_{0}B_{0}C_{0}

B_{0}C_{0}

C_{0}A_{0}

I

, respectively on points

A

B

C

, and the incircle of

\triangle ABC

I

BC

CA

AB

A_{1}

B_{1}

C_{1}

, respectively. We write with

\sigma (ABC)

\sigma (A_{1}B_{1}C_{1})

\triangle ABC

\triangle A_{1}B_{1}C_{1}

respectively. Prove that if

\sigma (ABC)=2 \sigma (A_{1}B_{1}C_{1})

AA_{0}

BB_{0}

CC_{0}

are concurrent.