MathDB

P20

Part of 2016 Sharygin Geometry Olympiad

Problems(1)

lines intersect on the incircle

Source: Sharygin Geometry Olympiad 2016 First Round P20 grades 10-11

7/25/2018
The incircle ω\omega of a triangle ABCABC touches BC,ACBC, AC and ABAB at points A0,B0A_0, B_0 and C0C_0 respectively. The bisectors of angles BB and CC meet the perpendicular bisector to segment AA0AA_0 at points QQ and PP respectively. Prove that PC0PC_0 and QB0QB_0 meet on ω\omega .
geometryincircleperpendicular bisector