MathDB

Reflections and circumcircle given, an angle equality wanted

Source: Turkey EGMO TST 2022 P1

March 16, 2022

geometrycircumcirclereflectiongeometric transformation

Problem Statement

Given an acute angle triangle

ABC

with circumcircle

\Gamma

and circumcenter

O

. A point

P

is taken on the line

BC

but not on

[BC]

. Let

K

be the reflection of the second intersection of the line

AP

and

\Gamma

with respect to

OP

. If

M

is the intersection of the lines

AK

and

OP

, prove that

\angle OMB+\angle OMC=180^{\circ}