If the radius of a circle is 30cm. Find the length of a chord which is 10cm from the center?

If the radius of a circle is 30cm. Find the length of a chord which is 10cm from the center?

Explanation

To find the length of the chord:

Let's denote the chord's length as 2x (since x would be half the chord's length due to symmetry).

The distance from the center to the chord is 10cm, forming a right triangle with hypotenuse 30cm (radius) and one leg 10cm (distance to chord).

The other leg (x) can be found using the Pythagorean theorem:

x² + 10² = 30²

x² + 100 = 900

x² = 800

x = √800 = √(400*2) = 20√2

The full chord's length is 2x = 2 * 20√2 = 40√2