Geometry

Question Analysis

The main focus is using the Pythagorean theorem in the right - triangle formed by the radius, the perpendicular from the center to the chord, and half of the chord.

 

Key Concept Explanation

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

 

Step - by - Step Solution

1. Let the radius  and the perpendicular distance from the center to the chord .

By the Pythagorean theorem,