MathDB

Given is triangle

ABC

with an inscribed circle with center

M

and radius

r

. The tangent to this circle parallel to

BC

intersects

AC

D

and

AB

E

. The tangent to this circle parallel to

AC

intersects

AB

F

and

BC

G

. The tangent to this circle parallel to

AB

intersects

BC

H

and

AC

K

. Name the centers of the inscribed circles of triangle

AED

, triangle

FBG

and triangle

KHC

successively

M_A, M_B, M_C

and the rays successively

r_A, r_B

and

r_C

. Prove that

r_A + r_B + r_C = r

Problem Statement