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.
To find the length of segment AP, we can use the Intersecting Secants Theorem, which states that when two secants intersect in a circle, the product of the segments of one secant is equal to the product of the segments of the other secant.
In this case, we have:
BP * PA = CP * PD
6 * PA = 7 * 12
6 * PA = 84
PA = 84 / 6
PA = 14
Therefore, the length of segment AP is 14.