MathDB

Spring 2020 Team Round Problem 6

Source:

August 22, 2020

Problem Statement

Let

\triangle ABC

be a triangle such that

AB=6, BC=8,

and

AC=10

. Let

M

be the midpoint of

BC

. Circle

\omega

passes through

A

and is tangent to

BC

at

M

. Suppose

\omega

intersects segments

AB

and

AC

again at points

X

and

Y

, respectively. If the area of

AXY

can be expressed as

\frac{p}{q}

where

p, q

are relatively prime integers, compute

p+q

.

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