You know the length of a chord and the distance it is from the center of a circle. How do you find the length of the radius?

Answer 1

Let's step through this one and knock it down. Draw a circle and a chord. Now add a radius to the circle that bisects the chord. It will form right angles with that chord, right? Yes, it will. Now add another radius from the center to one end of the chord where it intersects the circumference of the circle. You should have a right triangle, and one side is composed of half the length of the chord. The other side is that short segment between the chord and the center of the circle. The hypotenuse of the triangle is the radius of the circle, which is the last thing we drew in. Now let's do the math à la Pythagorus. You remember him. The sum of the squares of two sides of any right triangle is equal to the square of the hypotenuse. Yeah, that guy. You know the distance to the chord from the center of the circle. Put that on the drawing. You also know the chord length, and half of that will be the length of the other side of the right triangle you created. You have the lengths of two sides of the right triangle. Now square each side, add them together and take the square root of that to discover the length of the hypotenuse - which is the radius of the circle. Piece of cake. Want a sample problem? Why not. The length of a chord of a circle is 24 units. The chord is 5 units from the center of the circle. Remember our right triangle? It has side lengths of 5 units and 24 divided by 2 or 12 units. The 5 squared is 25 and the 12 squared is 144, and 25 plus 144 equals 169. The (positive) square root of 169 is 13, and our radius is 13 units long. Simple and easy. Just like Pythagoras or any of his students would handle the problem.

Answer 2

You can use the formula: ( r = \sqrt{h(2R - h)} ), where ( r ) is the radius, ( h ) is the distance from the center of the circle to the chord, and ( R ) is the length of the chord. Plug in the values you know to find the radius.