Geometry

Question Analysis

The main focus is to apply the Intersecting Chords Theorem. Given the lengths of three segments of the intersecting chords  and , we need to find the length of the fourth segment  by using the theorem's formula.

 

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