MathDB

2015-2016 Spring OMO #8

Source:

March 29, 2016

Online Math Open

Problem Statement

Let

EF

be a regular hexagon of side length

3

. Let

X, Y,

and

Z

be points on segments

AB, CD,

and

EF

such that

AX=CY=EZ=1

. The area of triangle

XYZ

can be expressed in the form

\dfrac{a\sqrt b}{c}

where

a,b,c

are positive integers such that

b

is not divisible by the square of any prime and

\gcd(a,c)=1

. Find

100a+10b+c

.
Proposed by James Lin

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