Geometry

Question Analysis

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

 

Key Concept Explanation

When a perpendicular line from the center of a circle to a chord is drawn, a right - triangle is formed. The radius of the circle is the hypotenuse, half of the chord length is one leg, and the distance from the center to the chord is the other leg. We use the Pythagorean theorem () to solve for the unknown side.

 

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:

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