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A circle centered at P with radius 10 and a circle centered at Q with radius 8 are externally tangent. A common external tangent intersects line PQ at R. Find QR.

 Feb 20, 2022
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Draw the picture.

Let XYR be the external tangent with X on circle(P) and Y on circle(Q).

Extend PQ to point R, the point of intersection of this line with the external tangent.

 

Triangle(XPR) is similar to triangle(YQR).   [Why?]

 

This makes:  RQ / RP  =  QY / PX  

 

Let x represent the length of RQ; then x + 18 represents the length of RP.

 

Therefore:  x / (x + 18)  =  8 / 10.

 

You will need to solve this equation.

 Feb 20, 2022

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