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concurrency with incircles defined by altitude in a right triangle

Source: Sharygin Geometry Olympiad 2016 First Round P9 grades 8-9

July 25, 2018

geometryincircleconcurrencyconcurrentright triangle

Problem Statement

Let

ABC

be a right-angled triangle and

CH

be the altitude from its right angle

C

. Points

O_1

and

O_2

are the incenters of triangles

ACH

and

BCH

respectively,

P_1

and

P_2

are the touching points of their incircles with

AC

and

BC

. Prove that lines

O_1P_1

and

O_2P_2

meet on

AB