Question

A chord of length 30cm is 8cm away from the center of the circle. What is the radius of the circle?

Answer 1

See a solution process below:

Explanation:

See picture below to explain the problem.

The chord is bisected by the ray from the center at a right angle and cuts the chord evenly in half.

Therefore, we can use the Pythagorean Theorem to determine the length of the radius for the circle described in the problem.

The Pythagorean Theorem states;

`c^2 = a^2 + b^2`

or

`c = sqrt(a^2 + b^2)`

Where:

• `c` is the length of the hypotenuse for a right triangle: what we are solving for in this problem.

• `a` is the length of one of the legs of the right right triangle: `(30" cm")/2 = 15" cm"` for this problem.

• `b` is the length of the other leg of the right right triangle: `8" cm"` for this problem.

Substituting and calculating `c` gives:

`c = sqrt(15^2 + 8^2)`

`c = sqrt(225 + 64)`

`c = sqrt(289)`

`c = 17`

The radius of the circle is `color(red)(17" cm")`