MathDB

Geometric inequality

Source: Sharygin CR P6(Grades 8-9)

March 4, 2022

Sharygin Geometry OlympiadSharygin 2022geometric inequalityinequalities

Problem Statement

The incircle and the excircle of triangle

ABC

touch the side

AC

at points

P

and

Q

respectively. The lines

BP

and

BQ

meet the circumcircle of triangle

ABC

for the second time at points

P'

and

Q'

respectively. Prove that

PP' > QQ'