MathDB

Let

ABC

be a triangle with

AB=2

and

AC=3

. Let

H

be the orthocenter, and let

M

be the midpoint of

BC

. Let the line through

H

perpendicular to line

AM

intersect line

AB

X

and line

AC

Y

. Suppose that lines

BY

and

CX

are parallel. Then

[ABC]^2=\frac{a+b\sqrt{c}}{d}

for positive integers

a,b,c

and

d

, where

\gcd(a,b,d)=1

and

c

is not divisible by the square of any prime. Compute

1000a+100b+10c+d

.
Proposed by Luke Robitaille

Problem Statement