MathDB

M2588

Part of Kvant 2019

Problems(1)

tangential and cyclic wanted, area of ABCD equals to MA x MC +MB x MD

Source: Tournament of Towns, Senior A-Level , Fall 2019 p5

4/18/2020
The point MM inside a convex quadrilateral ABCDABCD is equidistant from the lines ABAB and CDCD and is equidistant from the lines BCBC and ADAD. The area of ABCDABCD occurred to be equal to MA⋅MC+MB⋅MDMA\cdot MC +MB \cdot MD. Prove that the quadrilateral ABCDABCD is a) tangential (circumscribed), b) cyclic (inscribed).
(Nairi Sedrakyan)
tangentialcyclic quadrilateralCyclicgeometryareaKvant