MathDB

Let

ABC

be a triangle and

\ell

be a line parallel to

BC

that passes through vertex

A

. Draw two circles congruent to the circle inscribed in triangle

ABC

and tangent to line

\ell

AB

and

BC

(see picture). Lines

DE

and

FG

intersect at point

P

. Prove that

P

lies on

BC

if and only if

P

is the midpoint of

BC

.
(Mykhailo Plotnikov)
https://cdn.artofproblemsolving.com/attachments/8/b/2dacf9a6d94a490511a2dc06fbd36f79f25eec.png

Problem Statement