Circles w1 and w2 with centers at points O1 and O2 intersect at points A and B, respectively. Around the triangle O1O2B circumscribe a circle w centered at the point O, which intersects the circles w1 and w2 for the second time at points K and L, respectively. The line OA intersects the circles w1 and w2 at the points M and N, respectively. The lines MK and NL intersect at the point P. Prove that the point P lies on the circle w and PM=PN.(Vadym Mitrofanov) geometrycirclesequal segments