Geometry

Question Analysis

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

 

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 .

According to the Intersecting Chords Theorem,

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