Problem

Source: CWMO 2005-5

Tags: conics, hyperbola, geometry, geometric transformation, reflection, circumcircle, perpendicular bisector



Circles C(O1) and C(O2) intersect at points A, B. CD passing through point O1 intersects C(O1) at point D and tangents C(O2) at point C. AC tangents C(O1) at A. Draw AECD, and AE intersects C(O1) at E. Draw AFDE, and AF intersects DE at F. Prove that BD bisects AF.