Question

Examine the diagram, where the secant segment AP intersects the circle at points A and B, and the secant segment CP intersects the circle at points C and D. The lines intersect outside the circle at point P.
A circle, with no center shown, as described in the text. Segment A B equals 5, segment B P equals 7, and segment C P equals 14.

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

Answer 1

Answer: 6

Step-by-step explanation: I just got it correct.

Answer 2

Applying the intersecting secants theorem, the length of PD is: 6.

What is the Intersecting Secants Theorem?

The intersecting secants theorem states that if two secants intersect at a point outside a circle, then the product of the external secant secgent and the secant segment equals that of the other.

Given the following:

• AB = 5
• BP = 7
• CP = 14
• PD = ?

Based on the intersecting secants theorem, we would have:

AP × BP = CP × PD

Substitute

12 × 7 = 14 × PD

84 = 14(PD)

84/14 = PD

6 = PD

PD = 6

Therefore, applying the intersecting secants theorem, the length of PD is: 6.

Learn more about the intersecting secants theorem on:

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