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The two circles below are externally tangent.   A common external tangent intersects line $PQ$ at $R.$  Find $QR.$

 

 Feb 14, 2024
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Let  QR  =  4 + x

 

Let the radius of the larger circle be  PM

Let the radius of the smaller circle br QN

 

We can  construct similar triangles PMR  and  QNR  such that

 

PR / PM  = QR / QN

 

( 13 + x)  / 5 =  (4 + x)  / 4

 

4 (13 + x) =  5 (4 + x)

 

52 + 4x   = 20 + 5x

 

x = 32

 

QR =  4 + 32   =  36

 

 

cool cool cool

 Feb 14, 2024

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