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

 May 18, 2024
 #1
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The two circles below?

 

\(\overline{PQ}=\sqrt{(R+r)^2-(R-r)^2}=\sqrt{R^2+2Rr+r^2-R^2+2Rr-r^2}\\ \color{blue}\overline{PQ}=2 \sqrt{Rr}\)

laugh !

 May 18, 2024

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