MathDB

concurrecy, starting with reflections of incircle touchpoints to a given line

Source: Bulgaria 2009 NMO p2

May 28, 2019

geometryreflectionincircleconcurrencyconcurrent

Problem Statement

In the triangle

ABC

its incircle with center

I

touches its sides

BC, CA

and

AB

in the points

A_1, B_1, C_1

respectively. Through

I

is drawn a line

\ell

. The points

A', B'

and

C'

are reflections of

A_1, B_1, C_1

with respect to the line

\ell

. Prove that the lines

AA', BB'

and

CC'

intersects at a common point.