A chord is 80 inches long. It is 96 inches from the center of the circle. What is the radius of the circle?

104 inches

Step-by-step explanation:

To solve this, we use a circle theorem. The circle theorem to use is that a line from the center of a circle is perpendicular to a chord and it divides the chord into exactly two equal parts.

So therefore, we shall be having a right angled triangle if we join the edge of the chord to the center of the circle.

So in this circle, we have the distance from the center of the circle to the chord, the radius of the circle and half the length of the chord.

The length of the radius serves as the hypotenuse.

Let’s call the radius r.

The other two sides measure; 40 and 96 respectively.

Mathematically, using Pythagoras’ theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides;

r^2 = 40^2 + 96^2

r^2 = 10,816

r = √(10,816)

r = 104 inches

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