MathDB

Circles

\alpha

and

\beta

of the same radius intersect in two points, one of which is

P

. Denote by

A

and

B

, respectively, the points diametrically opposite to

P

on each of

\alpha

and

\beta

. A third circle of the same radius passes through

P

and intersects

\alpha

and

\beta

in the points

X

and

Y

, respectively. Show that the line

XY

is parallel to the line

AB

Problem Statement