MathDB

Let

ABC

be an acute triangle with

| AB | > | AC |

. Let

D

be the foot of the altitude from

A

BC

, let

K

be the intersection of

AD

with the internal bisector of angle

B

, Let

M

be the foot of the perpendicular from

B

CK

(it could be in the extension of segment

CK

) and

N

the intersection of

BM

and

AK

(it could be in the extension of the segments). Let

T

be the intersection of

AC

with the line that passes through

N

and parallel to

DM

. Prove that

BM

is the internal bisector of the angle

\angle TBC

Problem Statement