Question

select the correct answer.
which equation correctly describes the relationship between segment lengths in the given figure?
a. (fp)(gp) = (ep)(dp)
b. (fd)(fg) = (eg)(ed)
c. (fp)(fg) = (ep)(ed)
d. (fp)(dp) = (ep)(gp)

Explanation:

Step1: Recall the intersecting chords theorem

When two chords intersect each other inside a circle, the products of the lengths of their segments are equal.

Step2: Identify the segments of the intersecting chords

In the given circle, chords \(FD\) and \(EG\) intersect at point \(P\).
For chord \(FD\), the segments are \(FP\) and \(DP\).
For chord \(EG\), the segments are \(EP\) and \(GP\).

Step3: Apply the intersecting chords theorem

By the intersecting chords theorem, \((FP)(DP)=(EP)(GP)\)

Answer:

D. \((FP)(DP)=(EP)(GP)\)