MathDB

Let

ABC

be a triangle and

M

be the middle point of

BC

. Let

\Omega

be the circumference such as

A,B,C \in \Omega

. Let

P

be the intersection of

\Omega

and

AM

AF

is a hight of the triangle, with

F\in BC

, and

H

the orthocenter.Additionally the intersections of

MH

and

PF

with

\Omega

are

K

and

T

respectibly. Demonstrate that the circumscribed circumference of the traingle

KTF

is tangent with

BC

Problem Statement