MathDB

2021 Geo #5: Area Ratio

Source:

May 30, 2021

geometryratio

Problem Statement

Let

AE

be a triangle with

EF = 20

and

AE = AF = 21

. Let

AEF

and

D

be points chosen on segments

AE

and

AF,

respectively, such that

BD

is parallel to

EF.

Point

C

is chosen in the interior of triangle

AEF

such that

ABCD

is cyclic. If

BC = 3

and

CD = 4,

then the ratio of areas

\tfrac{[ABCD]}{[AEF]}

can be written as

\tfrac{a}{b}

for relatively prime positive integers

a, b

. Compute

100a + b

.

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