MathDB

Distinct points

A

B

and

C

lie on a line in this order. Point

D

lies on the perpendicular bisector of the segment

BC

. Denote by

M

the midpoint of the segment

BC

. Let

r

be the radius of the incircle of the triangle

ABD

and let

R

be the radius of the circle with center lying outside the triangle

ACD

, tangent to

CD

AC

and

AD

. Prove that

DM=r+R

2.