ITOT 41 Autumn 2019 - THPT A - Additive practice Question 5

An interior point M of a convex quadrilateral ABCD is equidistant from lines AB,CD and also equidistant from lines BC,AD. Its area equals $MA\cdot MC+MB\cdot MD$. Prove that ABCD (a) is cyclic; (b) has an incircle.