MathDB

Let

ABC

be an acute-angled triangle with circumscribed circle

k

and centre of the circumscribed circle

O

. A line through

O

intersects the sides

AB

and

AC

D

and

E

.Denote by

B'

and

C'

the reflections of

B

and

C

over

O

, respectively. Prove that the circumscribed circles of

ODC'

and

OEB'

concur on

k

Problem Statement