MathDB

Let point

I

be the center of the inscribed circle of an acute-angled triangle

ABC

. Rays

AI

and

BI

intersect the circumcircle

k

of triangle

ABC

at points

D

and

E

respectively. The segments

DE

and

CA

intersect at point

F

, the line through point

E

parallel to the line

FI

intersects the circle

k

at point

G

, and the lines

FI

and

DG

intersect at point

H

. Prove that the lines

CA

and

BH

touch the circumcircle of the triangle

DFH

at the points

F

and

H

respectively.

Problem Statement