MathDB

Let

ABCD

be a parallelogram in the plane. We draw two circles of radius

R

, one through the points

A

and

B

, the other through

B

and

C

. Let

E

be the other intersection point of the circles. We assume that

E

is not a vertex of the parallelogram. Show that the circle passing through

A, D

, and

E

also has radius

R

2