MathDB

Projective Fun

Source: 2018 AIME II #14

March 23, 2018

Problem Statement

The incircle of

\overline{AX}

of

\triangle ABC

is tangent to

\overline{BC}

at

X

. Let

Y \neq X

be the other intersection of

\overline{AX}

with

\omega

. Points

P

and

Q

lie on

\overline{AB}

and

\overline{AC}

, respectively, so that

\overline{PQ}

is tangent to

\omega

at

Y

. Assume that

AP=3, PB = 4, AC=8

, and

AQ = \tfrac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m+n

.

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