MathDB

lines intersect on the incircle

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

July 25, 2018

geometryincircleperpendicular bisector

Problem Statement

The incircle

\omega

of a triangle

ABC

touches

BC, AC

and

AB

at points

A_0, B_0

and

C_0

respectively. The bisectors of angles

B

and

C

meet the perpendicular bisector to segment

AA_0

at points

Q

and

P

respectively. Prove that

PC_0

and

QB_0

meet on

\omega