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TST IBERO 2023 CHILE

Source: TST IBERO 2023 CHILE

December 2, 2023

ChilegeometryIberoamericanTST

Problem Statement

Let

ABC

be a triangle with

AB < AC

and let

\omega

be its circumcircle. Let

M

denote the midpoint of side

BC

and

P

the midpoint of arc

Q

of

\omega

that contains

A

. The circumcircle of triangle

AMN

intersects sides

AB

and

AC

at points

P

and

Q

, respectively. Prove that

BP = CQ

.

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