Geometry

Question Analysis

The main focus is on the property that chords of equal length in a circle are equidistant from the center. We'll use this property to set up an equation involving the given expressions for the distances from the center to the chords and solve for .

 

Key Concept Explanation

In a circle, if two chords have the same length (both chords here are of length 25), then the perpendicular distances from the center of the circle to these chords are equal. This allows us to equate the expressions representing these distances.

 

Step - by - Step Solution

1. Since the two chords are of equal length, the distances from the center to the chords are equal. So, we set up the equation:

.

2. Add 3 to both sides of the equation to isolate the term with :

, which simplifies to

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