Geometry

Question Analysis

The main focus is to use the Intersecting Chords Theorem. We know the lengths of three segments of the intersecting chords  and , and we need to find the length of the fourth segment  by applying 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:

Given , , and

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