MathDB

rectangle, midpoints, right isoscles triangles, area wanted

Source: Mexican Mathematical Olympiad 1992 OMM P6

July 29, 2018

geometryrectanglearea

Problem Statement

ABCD

is a rectangle.

I

is the midpoint of

CD

BI

meets

AC

M

. Show that the line

DM

passes through the midpoint of

BC

E

is a point outside the rectangle such that

AE = BE

and

\angle AEB = 90^o

. If

BE = BC = x

, show that

EM

bisects

\angle AMB

. Find the area of

AEBM

in terms of

x