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2023 MOAA Gunga P15

Source:

October 15, 2023

MOAA 2023

Problem Statement

Triangle

ABC

has

AB = 5

,

BC = 7

,

CA = 8

. Let

M

be the midpoint of

BC

and let points

P

and

Q

lie on

AB

and

AC

respectively such that

MP \perp AB

and

MQ \perp AC

. If

H

is the orthocenter of

\triangle{APQ}

then the area of

\triangle{HPM}

can be expressed in the form

\frac{a\sqrt{b}}{c}

where

a

and

c

are relatively prime positive integers and

b

is square-free. Find

a+b+c

.
Proposed by Harry Kim

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