Geometry

Question Analysis

The main focus is on leveraging the Pythagorean theorem to determine the distance from the center of the circle to the chord and then using that result to find the value of based on the radius.

 

Key Concept Explanation

When a perpendicular is drawn from the center of a circle to a chord, a right - triangle is formed. The radius of the circle serves as the hypotenuse, half of the chord length is one leg, and the distance from the center to the chord is the other leg. The Pythagorean theorem () is applied to relate these sides.

 

Step - by - Step Solution

1. First, find the distance from the center of the circle to the chord.

Let the radius and half of the chord length . Denote the distance from the center to the chord as .

According to the Pythagorean theorem, .

Substitute and into the formula:

Click "Show Answer" to reveal the answer and analysis