Geometry

Question Analysis

The main focus is to correctly apply the Intersecting Chords Theorem. Given expressions for the lengths of segments of the intersecting chords and , we need to set up an equation using the theorem to solve for .

 

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

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