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T,H,E,B are concyclic

Source: Tuymaada 2024 Junior P4

July 10, 2024

geometry

Problem Statement

A triangle

ABC

is given.

N

and

M

are the midpoints of

AB

and

BC

, respectively. The bisector of angle

B

meets the segment

MN

at

E

.

H

is the base of the altitude drawn from

B

in the triangle

ABC

. The point

T

on the circumcircle of

ABC

is such that the circumcircles of

TMN

and

ABC

are tangent. Prove that points

T, H, E, B

are concyclic. Proposed by M. Yumatov

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