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starting with 3 right triangles, find area of a quadrilateral

Source: Mexican Mathematical Olympiad 1993 OMM P1

July 29, 2018

geometryarea of a triangleright triangles

Problem Statement

ABC

is a triangle with

\angle A = 90^o

. Take

E

such that the triangle

AEC

is outside

ABC

and

AE = CE

and

\angle AEC = 90^o

. Similarly, take

D

so that

ADB

is outside

ABC

and similar to

AEC

.

O

is the midpoint of

BC

. Let the lines

OD

and

EC

meet at

D'

, and the lines

OE

and

BD

meet at

E'

. Find area

DED'E'

in terms of the sides of

ABC

.

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