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, we need to use this property to set up an equation based on the given expressions for the two segments of the chord.

 

Key Concept Explanation

In a circle, if a diameter is perpendicular to a chord, the diameter divides the chord into two equal - length segments. This allows us to equate the expressions representing 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. Move the  terms to one side and the constant terms to the other side:

Subtract  from both sides: , which simplifies to

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