MathDB

R is incenter of CST wanted, right triangle, point symmetric wrt side

Source: Champions Tournament (Ukraine) - Турнір чемпіонів - 2008 Seniors p2

September 7, 2020

geometryincenterright triangleChampions Tournament

Problem Statement

Given a right triangle

ABC

with

\angle C=90^o

. On its hypotenuse

AB

is arbitrary mark the point

P

. The point

Q

is symmetric to the point

P

wrt

AC

. Let the lines

PQ

and

BQ

intersect

AC

at points

O

and

R

respectively. Denote by

S

the foot of the perpendicular from the point

R

on the line

AB

(

S \ne P

), and let

T

be the intersection point of lines

OS

and

BR

. Prove that

R

is the center of the circle inscribed in the triangle

CST