Let Γ1 and Γ2 be two circles of unequal radii, with centres O1 and O2 respectively, intersecting in two distinct points A and B. Assume that the centre of each circle is outside the other circle. The tangent to Γ1 at B intersects Γ2 again in C, different from B; the tangent to Γ2 at B intersects Γ1 again at D, different from B. The bisectors of ∠DAB and ∠CAB meet Γ1 and Γ2 again in X and Y, respectively. Let P and Q be the circumcentres of triangles ACD and XAY, respectively. Prove that PQ is the perpendicular bisector of the line segment O1O2.Proposed by Prithwijit De Spiral Similaritycirclesgeometrydumpty point