Geometry

Question Analysis

The main focus is on the property of chords in a circle. When a diameter is perpendicular to a chord, it bisects the chord. Here, the given expressions represent the lengths of the two segments of the chord that is bisected by the diameter.

 

Key Concept Explanation

In a circle, if a diameter is perpendicular to a chord, then the diameter divides the chord into two equal - length segments. This property allows us to set up an equation based on the given expressions for the lengths of these segments.

 

Step - by - Step Solution

1. Since the diameter is perpendicular to the chord, the two segments of the chord are equal. So, we set up the equation:

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2. First, move the  terms to one side and the constant terms to the other side:

Subtract  from both sides: , which simplifies to