Problem:
The two circles below are externally tangent. A common external tangent intersects line \(PQ\) at \(R\) Find \(QR\).
+1632 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
