Geometry

Question Analysis

The main focus is on using the relationship between a chord, the perpendicular from the center to the chord, and the radius of the circle. We'll apply the Pythagorean theorem to find the value of  (the radius).

 

Key Concept Explanation

When a line from the center of a circle is perpendicular to a chord, it bisects the chord. In the right - triangle formed by the radius (hypotenuse), half of the chord, and the perpendicular from the center to the chord, we can use the Pythagorean theorem , where  is the radius and ,  are the other two sides.

 

Step - by - Step Solution

1. Since the perpendicular from the center to the chord bisects the chord, and here the given length  is half of the chord.

2. Let the perpendicular distance from the center to the chord  and half of the chord length .

3. Apply the Pythagorean theorem:

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