Question

56:41
A circle is shown. Secant P N and tangent M N intersect at point N outside of the circle. Secant P N intersects the circle at point Q. The length of M N is 6, the length of Q N is 4, and the length of P Q is x.

What is the length of line segment PQ?

4 units
5 units
6 units
9 units

Answer 1

Use the tangent-secant power theorem: (tangent length)^2 = (external secant segment)·(whole secant length). Here MN^2 = NQ · NP, and NP = NQ + PQ = 4 + x.

So 6^2 = 4(4 + x) → 36 = 16 + 4x → 4x = 20 → x = 5.

Answer: 5 units.