2017 UNCO Math Contest II Problems/Problem 1

Problem

$[asy] pair A=24*dir(40),B=15*dir(220); pair C1=(0,0),C2=(52,0); draw(circle(C1,24),black); draw(circle(C2,15),black); draw(C1--C2,dot); draw(A--(B+C2)); [/asy]$

A circle has radius 24, a second circle has radius 15, and the centers of the two circles are 52 units apart. A line tangent to both circles crosses the line connecting the two centers at a point P between the two centers. How much farther is P from the center of the bigger circle than it is from the center of the smaller circle?

Solution

$12$

2017 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by First Question	Followed by Problem 2
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All UNCO Math Contest Problems and Solutions

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2017 UNCO Math Contest II Problems/Problem 1

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Solution

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