MathDB

From a point

P

exterior to a circle

K

, two rays are drawn intersecting

K

in the respective pairs of points

A, A'

and

B,B'

. For any other pair of points

C, C'

K

, let

D

be the point of intersection of the circumcircles of triangles

PAC

and

PB'C'

other than point

P

. Similarly, let

D'

be the point of intersection of the circumcircles of triangles

PA'C'

and

PBC

other than point

P

. Prove that the points

P, D

, and

D'

are collinear.

Problem Statement