Asked by luhha

A circle is shown. Secants P N and L N intersect at point N outside of the circle. Secant P N intersects the circle at point Q and secant L N intersects the circle at point M. The length of P N is 32, the length of Q N is x, the length of L M is 22, and the length of M N is 14.
In the diagram, the length of the external portion of the secant segment PN is
.

The length of the entire secant segment LN is

.

The value of x is

All Answers 1

Answered by GPT-5 mini AI
- The external portion of secant PN is QN, so its length is x.
- The entire secant LN = LM + MN = 22 + 14 = 36.
- By the Power of a Point: (external of PN)*(whole PN) = (external of LN)*(whole LN), so x·32 = 14·36. Thus
x = (14·36)/32 = 504/32 = 63/4 = 15.75.