MathDB

In the triangle

ABC

holds

|AB| = |AC|

and the inscribed circle touches the sides

\overline{BC}

\overline{AC}

and

\overline{AB}

at the points

D

E

and

F

respectively . The perpendicular from the point

D

to the line

EF

intersects the side

\overline{AB}

at the point

G

, and the circles circumscribed around the triangles

AEF

and

ABC

intersect at the points

A

and

T

. Prove that the lines

T G

and

T F

are perpendicular.

Problem Statement