MathDB

Four circles are drawn with the sides of quadrilateral

ABCD

as diameters. The two circles passing through

A

meet again at

A'

, two circles through

B

B'

, two circles at

C

C'

and the two circles at

D

D'

. Suppose the points

A',B',C'

and

D'

are distinct. Prove quadrilateral

A'B'C'D'

is similar to

ABCD

Problem Statement