Question

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

B, PQ = 5 units.

Explanation:

Just scored 100% on the test.

Answer 2

`PQ=5\ units`

Explanation:

we know that

The Intersecting Secant-Tangent Theorem, states that : If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

so

In this problem

`MN^2=(PN)(QN)`

we have

`MN=6\ units\\PN=PQ+QN=(x+4)\ units\\QN=4\ units`

substitute the given values

`6^2=(x+4)(4)`

solve for x

`36=4x+16\\4x=36-16\\4x=20\\x=5\ units`

therefore

`PQ=5\ units`