Geometry

Question Analysis

The main focus is to apply the Intersecting Chords Theorem correctly. We are given the lengths of three segments of the intersecting chords and need to find the length of the fourth segment  by using the appropriate formula derived from the theorem.

 

Key Concept Explanation

Intersecting Chords Theorem: When two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal. That is, if chords  and  intersect at point , then .

 

Step - by - Step Solution

1. Set up the equation using the theorem:

We know that , , and