MathDB

Bisector and altitude relations

Source: Turkey TST 2019 Day 1 P3

March 26, 2019

geometry

Problem Statement

In a triangle

ABC

,

AB>AC

. The foot of the altitude from

A

to

BC

is

D

, the intersection of bisector of

B

and

AD

is

K

, the foot of the altitude from

B

to

CK

is

M

and let

BM

and

AK

intersect at point

N

. The line through

N

parallel to

DM

intersects

AC

at

T

. Prove that

BM

is the bisector of angle

\widehat{TBC}

.

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