Question

Circle P is shown. Line segment P Q is a radius and has a length of 9. Line Q R is a tangent that intersects the circle at point Q and has a length of 12. A line connects points R and P. The distance between point R and the circle is x, and the point on the circle to point P is a radius.
What value of x would make Line R Q tangent to circle P at point Q?

x =

Answer 1

Because a radius to a tangent is perpendicular, triangle PQR is a right triangle with legs 9 and 12. By Pythagoras PR = sqrt(9^2 + 12^2) = 15. The distance from R to the circle is PR − radius = 15 − 9 = 6.

x = 6