MathDB

Let

k

be a circle with diameter

AB

and centre

O

. Let C be an arbitrary point on the circle different from

A

and

B

. Let

D

be the point for which

O

B

D

and

C

(in this order) are the four vertices of a parallelogram. Let

E

be the intersection of the line

BD

and the circle

k

, and let

F

be the orthocenter of the triangle

OAC

. Prove that the points

O, D, E, C, F

lie on a circle.

Problem Statement