MathDB

2017-2018 Spring OMO Problem 14

Source:

April 3, 2018

Problem Statement

Let

ABC

be a triangle with

AB=20

and

AC=18

.

E

is on segment

AC

and

F

is on segment

AB

such that

AE=AF=8

. Let

BE

and

CF

intersect at

G

. Given that

AEGF

is cyclic, then

BC=m\sqrt{n}

for positive integers

m

and

n

such that

n

is not divisible by the square of any prime. Compute

100m+n

.
Proposed by James Lin

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