MathDB

BD _|_ CE , DEFO rhombus, ABC equilateral

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2022 p1

March 26, 2024

geometryrhombusperpendicularperpendicularity

Problem Statement

Let

\Gamma

be a circle with center

O

. Consider the points

A

B

C

D

E

and

F

\Gamma

, with

D

and

E

in the (minor) arc

BC

and

C

in the (minor) arc

EF

, such that

DEFO

is a rhombus and

\vartriangle ABC

It is equilateral. Show that

\overleftrightarrow{BD}

and

\overleftrightarrow{CE}

are perpendicular.