MathDB

4

Part of 2023 Bulgaria National Olympiad

Problems(1)

Bash Bash Bash

Source: Bulgaria National Olympiad 2023 Problem 4

4/9/2023
Prove that there exists a unique point MM on the side ADAD of a convex quadrilateral ABCDABCD such that SABM+SCDM=SABCD\sqrt{S_{ABM}}+\sqrt{S_{CDM}} = \sqrt{S_{ABCD}} if and only if AB∥CDAB\parallel CD.
geometryareaconvex quadrilateral