MathDB

tangent (ACE) and (BDM), <B = 3<C

Source: 2023 IGO Intermediate P3

January 18, 2024

geometrytangent circles

Problem Statement

Let

\omega

be the circumcircle of the triangle

ABC

with

\angle B = 3\angle C

. The internal angle bisector of

\angle A

, intersects

\omega

and

BC

at

M

and

D

, respectively. Point

E

lies on the extension of the line

MC

from

M

such that

ME

is equal to the radius of

\omega

. Prove that circumcircles of triangles

ACE

and

BDM

are tangent.
Proposed by Mehran Talaei - Iran

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