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Problem:

 

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

 


 

 Jan 8, 2023
 #2
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Guest, please stop posting random answers. 

We know PQ is 18, and by pythagorean theorem, we can conclude that RS (the points of tangency of circles P and Q respectively) has length sqrt(18^2 - 2^2). sqrt(320) simplifies to 8sqrt(5). (unnessecary but you can do it this way)

Let QR = x. By similar triangles, x/8 = (x + PQ)/10

10x = 8x + 8*18

2x = 144

x = 72 = QR

 Jan 9, 2023
 #3
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The correct answer is actually 90, but thanks for the help!

Guest Jan 10, 2023
 #4
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So is it 72 or 90?
 

Edit: It's 72. Thank you for the help.

Guest Jan 15, 2023
edited by Guest  Jan 15, 2023

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