Problem 5 of Fourth round
Source: VII International Festival of Young Mathematicians Sozopol 2016, Theme for 10-12 grade
September 3, 2019
geometry
Problem Statement
A convex quadrilateral is cut into smaller convex quadrilaterals so that they are adjacent to each other only by whole sides.
a) Prove that if all small quadrilaterals are inscribed in a circle, then the original one is also inscribed in a circle.
b) Prove that if all small quadrilaterals are cyclic, then the original one is also cyclic.