MathDB

Let

ABC

be an acute-angled triangle and let

E

and

F

be the feet of the altitudes from

B

and

C

to the sides

AC

and

AB

respectively. Suppose

AD

is the diameter of the circle

ABC

. Let

M

be the midpoint of

BC

. Let

K

be the imsimilicenter of the incircles of the triangles

BMF

and

CME

. Prove that the points

K, M, D

are collinear.
Proposed by Bilegdembrel Bat-Amgalan.

Problem Statement