MathDB

On the side

BC

of the parallelogram

ABCD

, points

E

and

F

are given (

E

lies between

B

and

F

) and the diagonals

AC, BD

meet at

O

. If it's known that

AE, DF

are tangent to the circumcircle of

\triangle AOD

, prove that they're tangent to the circumcircle of

\triangle EOF

as well.

Problem Statement