MathDB

Let

AB

be a triangle and

\Gamma

the excircle, relative to the vertex

A

, with center

D

. The circle

\Gamma

is tangent to the lines

AB

and

AC

E

and

F

, respectively. Let

P

and

Q

be the intersections of

EF

with

BD

and

CD

, respectively. If

O

is the point of intersection of

BQ

and

CP

, show that the distance from

O

to the line

BC

is equal to the radius of the inscribed circle in the triangle

ABC

Problem Statement