MathDB

Spring 2020 Team Round Problem 14

Source:

August 22, 2020

Problem Statement

Let

\triangle ABC

be a triangle such that

AB=40

and

AC=30.

Points

X

and

Y

are on the segment

AB

and

BC,

respectively such that

AX:BX=3:2

and

BY:CY=1:4.

Given that

XY=12,

the area of

\triangle ABC

can be written as

a\sqrt{b}

where

a

and

b

are positive integers and

b

is squarefree. Compute

a+b.

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