A circle has a radius of 13 cm with a chord 12 cm away from the centre of the circle. Calculate the length of the chord.

Answer Details

To calculate the length of the chord in a circle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we can consider the radius of the circle as one side of the right triangle, the distance from the center of the circle to the chord as the other side, and the chord itself as the hypotenuse.

Let's denote the radius as r, the distance from the center to the chord as d, and the length of the chord as c.

Using the Pythagorean theorem, we have:

r² = d² + (c/2)²

Since we know the value of the radius (13 cm) and the distance from the center to the chord (12 cm), we can substitute those values into the equation:

13² = 12² + (c/2)²

Simplifying the equation, we get:

169 = 144 + (c/2)²

Subtracting 144 from both sides, we have:

25 = (c/2)²

Taking the square root of both sides, we get:

5 = c/2

Multiplying both sides by 2, we find:

c = 10 cm

Therefore, the length of the chord in the circle is 10 cm.