criterion for a convex hexagon with parallel opposite sides to be cyclic
Source: 2008 Oral Moscow Geometry Olympiad grades 8-9 p6
October 13, 2020
geometryhexagonparallelCyclic
Problem Statement
Opposite sides of a convex hexagon are parallel. Let's call the "height" of such a hexagon a segment with ends on straight lines containing opposite sides and perpendicular to them. Prove that a circle can be circumscribed around this hexagon if and only if its "heights" can be parallelly moved so that they form a triangle.(A. Zaslavsky)