How to Find the Radius of a Circle with a Chord

To find the radius of a circle when you know the length of a chord and the distance from the center of the circle to the chord, you can use a simple geometric approach.

Here’s a step-by-step explanation:

1. Identify the Components: Let’s denote the chord length as c and the distance from the center of the circle to the chord as d.
2. Half the Chord: Since the radius, the distance to the chord, and half the chord form a right triangle, first find half the chord length, which is c/2.
3. Use the Pythagorean Theorem: In the right triangle formed, the radius r is the hypotenuse, and the other two sides are d and c/2. Therefore, you can use the Pythagorean theorem:
• r² = d² + (c/2)²
4. Calculate the Radius: Rearranging the formula, you’ll calculate the radius as:
• r = √(d² + (c/2)²)

This formula gives you the radius of the circle based on the chord length and the distance from the circle’s center to that chord. Just plug in your values for c and d, and you’ll have the radius!