MathDB

Problem 9.3

Part of 2007 Bulgarian Autumn Math Competition

Problems(1)

Cyclic quads wanted

Source: 2007 Bulgarian Autumn Math Competition, Problem 9.3

3/17/2022
Let the intersection of the diagonals ACAC and BDBD of the convex quadrilateral ABCDABCD be point EE. Let MM be the midpoint of AEAE and NN be the midpoint of CDCD. It's known that BDBD bisects ∠ABC\angle ABC. Prove that ABCDABCD is cyclic if and only if MBCNMBCN is cyclic.
geometrycyclic quadrilateral