MathDB

Let

M

be a point on the altitude

CD

of an acute-angled triangle

ABC

, and

K

and

L

the orthogonal projections of

M

AC

and

BC

. Suppose that the incenter and circumcenter of the triangle lie on the segment

KL

.
(a) Prove that

CD=R+r

, where

R

and

r

are the circumradius and inradius, respectively. (b) Find the minimum value of the ratio

CM:CD

Problem Statement