Question

Let ABCD be a cyclic quadrilateral, and let the diagonals meet in point S. From S, draw perpendiculars to the four sides, with feet L on AB, M on BC, N on CD and K on DA. This gives a new quadrilateral LM N K. Prove that the sum of two opposite angles in this new quadrilateral is double the corresponding angle at the intersection S. (E.g.∠L+∠N= 2∠ASB). Hint: Find four smaller cyclic quadrilaterals in the diagram.

Answer 1