MathDB

PB = PC , 2 circumcenters related

Source: 2015 Cuba 2.8

September 20, 2024

geometrycircumcircle

Problem Statement

Let

ABC

be an acute triangle and

D

be the foot of the altiutude from

A

on

BC

,

E

and

F

are the midpoints of

BD

and

DC

respectively.

O

and

Q

are the circumcenters of the triangles

\vartriangle BF

and

\vartriangle ACE

respectively.

P

is the intersection point of

OE

and

QF

, show that

PB = PC

.

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