MathDB

EO _|_ ZD wanted, rectangle, equilateral, equal extensions related

Source: 2011 Indonesia MO Province P2 q4 OSP

December 10, 2020

geometryrectangle

Problem Statement

Given a rectangle

ABCD

with

AB = a

and

BC = b

. Point

O

is the intersection of the two diagonals. Extend the side of the

BA

so that

AE = AO

, also extend the diagonal of

BD

so that

BZ = BO.

Assume that triangle

EZC

is equilateral. Prove that (i)

b = a\sqrt3

(ii)

EO

is perpendicular to

ZD