MathDB

prove that H is the incenter of triangle PQT

Source: 2012 Sharygin Geometry Olympiad Final Round 9.8

August 3, 2018

geometryincenter

Problem Statement

Let

AH

be an altitude of an acute-angled triangle

ABC

. Points

K

and

L

are the projections of

H

onto sides

AB

and

AC

. The circumcircle of

ABC

meets line

KL

at points

P

and

Q

, and meets line

AH

at points

A

and

T

. Prove that

H

is the incenter of triangle

PQT

.
(M.Plotnikov)