Geometry

Question Analysis

The main focus is 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 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, half of the chord length is . The perpendicular distance from the center to the chord is .

2. Apply the Pythagorean theorem: