Problem

Source: 2022 Czech-Polish-Slovak Match Junior, individual p3 CPSJ

Tags: geometry, pentagon



Given is a convex pentagon $ABCDE$ in which $\angle A = 60^o$, $\angle B = 100^o$, $\angle C = 140^o$. Show that this pentagon can be placed in a circle with a radius of $\frac23 AD$.