MathDB

Let

ABC

be a triangle. Let

D

be the intersection point of the angle bisector at

A

with

BC

. Let

T

be the intersection point of the tangent line to the circumcircle of triangle

ABC

at point

A

with the line through

B

and

C

. Let

I

be the intersection point of the orthogonal line to

AT

through point

D

with the altitude

h_a

of the triangle at point

A

. Let

P

be the midpoint of

AB

, and let

O

be the circumcenter of triangle

ABC

. Let

M

be the intersection point of

AB

and

TI

, and let

F

be the intersection point of

PT

and

AD

. Prove:

MF

and

AO

are orthogonal to each other.

Problem Statement