MathDB

Let

ABC

be a triangle and let

D

be a point in the interior of the triangle which lies on the angle bisector of

\angle BAC

. Suppose that lines

BD

and

AC

meet at

E

, and that lines

CD

and

AB

meet at

F

. The circumcircle of

ABC

intersects line

EF

at points

P

and

Q

. Show that if

O

is the circumcenter of

DPQ

, then

OD

is perpendicular to

BC

.
Michael Ren

Problem Statement