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.

Guest Feb 20, 2022

#1**+1 **

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.

geno3141 Feb 20, 2022