Geometry

Question Analysis

The main focus is using the property that when a diameter is perpendicular to a chord, it bisects the chord. We'll set up an equation based on the expressions for the two segments of the chord to find the value of .

 

Key Concept Explanation

In a circle, a diameter perpendicular to a chord divides the chord into two equal parts. This allows us to equate the lengths of the two segments represented by the given algebraic expressions.

 

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:

.

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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