MathDB

concyclic wanted, <PXM=<PYM, PA// BC, starting with isosceles

Source: 2019 Croatia MO p3

August 2, 2020

geometryConcyclicisoscelesequal angles

Problem Statement

Given an isosceles triangle

ABC

such that

|AB|=|AC|

. Let

M

be the midpoint of the segment

BC

and let

P

be a point other than

A

such that

PA\parallel BC

. The points

X

and

Y

are located respectively on rays

PB

and

PC

, so that the point

B

is between

P

and

X

, the point

C

is between

P

and

Y

and

\angle PXM=\angle PYM

. Prove that the points

A,P,X

and

Y

are concyclic.

Back to Problems View on AoPS