Question

Examine the diagram, where AB←→ is secant to the circle at points A and B, and CD←→ is secant to the circle at points C and D. The lines intersect inside the circle at point P, which is not the center.
A circle with no center shown and two secants as described in the text. Segment B P equals 6, segment C P equals 7, and segment D P equals 12.


What is the length of AP¯¯¯¯¯¯¯¯?
Enter the correct value.

Answer 1

In the secant secant theorem,

AP × BP = CP × DP

AP × 6 = 7 × 12

AP = 7 × 2 = 14

Answer: 14