MathDB

Let

\mathcal C

be a circle centered at

O

and

A\ne O

be a point in its interior. The perpendicular bisector of the segment

OA

meets

\mathcal C

at the points

B

and

C

, and the lines

AB

and

AC

meet

\mathcal C

again at

D

and

E

, respectively. Show that the circles

(OBC)

and

(ADE)

have the same centre.
Ion Pătrașcu, Ion Cotoi

Problem Statement