Problem:

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

Guest Jan 8, 2023

#2**+1 **

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

proyaop Jan 9, 2023