IMO 2020 Shortlist G3
Let ABCD be a convex quadrilateral with =ABC ą 90˝ , =CDA ą 90˝ , and =DAB “ =BCD. Denote by E and F the reflections of ...
Category: Geometry
Problem
Let ABCD be a convex quadrilateral with =ABC ą 90˝ , =CDA ą 90˝ , and =DAB “ =BCD. Denote by E and F the reflections of A in lines BC and CD, respectively. Suppose that the segments AE and AF meet the line BD at K and L, respectively. Prove that the circumcircles of triangles BEK and DFL are tangent to each other. (Slovakia)