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Source: 2016 AIME II #10

March 17, 2016

AMCAIMEAIME II2016 AIME II

Problem Statement

Triangle

ABC

is inscribed in circle

\omega

. Points

P

and

Q

are on side

\overline{AB}

with

AP<AQ

. Rays

CP

and

CQ

meet

\omega

again at

S

and

T

(other than

C

), respectively. If

AP=4,PQ=3,QB=6,BT=5,

and

AS=7

, then

ST=\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m+n

.

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