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1) Circle O is a unit circle. Segment AS has length (12/5) and is tangent to circle O at A. If P is the intersection of OS with circle O, find length PS.

Image: https://latex.artofproblemsolving.com/c/5/c/c5c4f75055dc61926bbe16dd03aff9a27c08d98e.png

 

2) Two circles, centered at A and B are externally tangent to each other, and tangent to a line L. A third circle, centered at C is externally tangent to the first two circles, and the line L. If the radii of circle A and circle B are 9 and 16, respectively, then what is the radius of circle C.

Image: https://latex.artofproblemsolving.com/4/d/a/4da24a4edb9693476d2766d290f52dd917498a6f.png

 Mar 3, 2019
 #1
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+1

1.

 

Since AS is tangent to the circle  triangle AOS is a right triangle and  AO = 1....then OS =  sqrt [ (12/5)^2 + 1 ] = sqrt [ 144/25 + 1 ] =

 

sqrt [  144/25 + 25/25 ] =   sqrt [ 169 / 25 ] =  13/5

 

So....

 

OS - OP = PS

 

13/5 - 1 = PS

 

13/5 - 5/5 = PS

 

8 / 5  =  PS

 

 

cool cool cool

 Mar 3, 2019

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