MathDB

Areas with an inscribed pentagon

Source: 2023 4th OMpD L3 P2 - Brazil - Olimpíada Matemáticos por Diversão

September 21, 2023

geometrypentagonconvex polygonareasInscribed Figures

Problem Statement

Let

ABCDE

be a convex pentagon inscribed in a circle

\Gamma

, such that

AB = BC = CD

. Let

F

and

G

be the intersections of

BE

with

AC

and of

CE

with

BD

, respectively. Show that:
a)

[ABC] = [FBCG]

\frac{[EFG]}{[EAD]} = \frac{BC}{AD}

Note:

[X]

denotes the area of polygon

X