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equal segments starting with the incircle of a right triangle

Source: 2014 Sharygin Geometry Olympiad Final Round 8.1

August 3, 2018

geometryright triangle

Problem Statement

The incircle of a right-angled triangle

ABC

touches its catheti

AC

and

BC

at points

B_1

and

A_1

, the hypotenuse touches the incircle at point

C_1

. Lines

C_1A_1

and

C_1B_1

meet

CA

and

CB

respectively at points

B_0

and

A_0

. Prove that

AB_0 = BA_0

.
(J. Zajtseva, D. Shvetsov )