MathDB

P9

Part of 2016 Sharygin Geometry Olympiad

Problems(1)

concurrency with incircles defined by altitude in a right triangle

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

7/25/2018
Let ABCABC be a right-angled triangle and CHCH be the altitude from its right angle CC. Points O1O_1 and O2O_2 are the incenters of triangles ACHACH and BCHBCH respectively, P1P_1 and P2P_2 are the touching points of their incircles with ACAC and BCBC. Prove that lines O1P1O_1P_1 and O2P2O_2P_2 meet on ABAB.
geometryincircleconcurrencyconcurrentright triangle