Geometry

Question Analysis

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

 

Key Concept Explanation

In a circle, when two chords are equidistant from the center (shown by the equal markings from the center to the chords), their lengths are equal. This allows us to equate the algebraic expressions representing the lengths of these chords.

 

Step - by - Step Solution

1. Since the two chords are equidistant from the center, their lengths are equal. So, we set up the equation:

.

2. Move the  terms to one side and the constant terms to the other side:

Subtract  from both sides: , which simplifies to .

Then add 19 to both sides:

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