MathDB

Triangle

ABC

is given. Let

O

be it's circumcenter. Let

I

be the center of it's incircle.The external angle bisector of

A

meet

BC

D

. And

I_A

is the

A

-excenter . The point

K

is chosen on the line

AI

such that

AK=2AI

and

A

is closer to

K

than

I

. If the segment

DF

is the diameter of the circumcircle of triangle

DKI_A

, then prove

OF=3OI

Problem Statement