MathDB

2021 USMCA National Championship #8

Source:

May 9, 2021

Problem Statement

Let

ABCD

be a parallelogram with

AB=CD=16

and

BC=AD=24.

Suppose the angle bisectors of

\angle A

and

\angle D

intersect

BC

at

E

and

100,

respectively. Moreover, suppose

AE

and

DF

intersect at

P.

Given that the sum of the areas of quadrilaterals

ABFP

and

DCEP

is

100,

compute the area of the parallelogram.

Back to Problems View on AoPS