Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
If a chord 10 inches long is 5 inches from the center of a circle, find the radius of the circle.

x =

Answer 1

Remark

I hope all you want is the radius of the circle. If you want more, we'll need the pictures.

If a chord is 10 inches long, then the distance from the center of the chord the center of the circle is given as 5 inches. Distance in this instance is thought of as the shortest distance from the center of the circle to the chord. Thus 5 inches.

The center of the chord to the center of the circle is one side of a right triangle. 1/2 the distance of the chord is another side of a right triangle. The radius is the third side.

Givens

a = 5

b = 5

c = ??

Formula

a^2 + b^2 = c^2

Sub and solve

c^2 = 5^2 + 5^2

c^2 = 25 + 25 Combine the right

c^2 = 50 Take the square root of both sides.

sqrt(c^2) = sqrt(50)

sqrt(c^2) = sqrt(25 * 2)

sqrt(c^2) = sqrt(25) * sqrt(2)

c = 5 * sqrt(2) = radius <<<<< Answer.