MathDB

Equilateral triangle geo

Source: Iberoamerican 2022, Day 1, P1

September 29, 2022

geometry

Problem Statement

Given is an equilateral triangle

ABC

with circumcenter

O

. Let

D

be a point on to minor arc

BC

of its circumcircle such that

DB>DC

. The perpendicular bisector of

OD

meets the circumcircle at

E, F

, with

E

lying on the minor arc

BC

. The lines

BE

and

CF

meet at

P

. Prove that

PD \perp BC

.

Back to Problems View on AoPS