Geometry

Question Analysis

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

 

Key Concept Explanation

In a circle, when two chords have the same length (both chords here are of length 23), 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 11 to both sides of the equation to isolate the term with :

, which simplifies to

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