MathDB

Concurency on center line

Source: Iberoamerican Problem 4

September 22, 2017

geometrycircumcircleconcurrencyIberoamerican

Problem Statement

Let

ABC

be an acute triangle with

AC > AB

and

O

its circumcenter. Let

D

be a point on segment

BC

such that

O

lies inside triangle

ADC

and

\angle DAO + \angle ADB = \angle ADC

. Let

P

and

Q

be the circumcenters of triangles

ABD

and

ACD

respectively, and let

M

be the intersection of lines

BP

and

CQ

. Show that lines

AM, PQ

and

BC

are concurrent.
Pablo Jaén, Panama

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