wo chords are drawn in the circle such that one chord is 24 cm away from the centre and other is 10 cm away from the centre. If the radius of the circle is 26 cm, find the length of the chords.

To find the length of the chords, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

Here, the hypotenuse is the radius of the circle (26 cm), and the other two sides are the distance of the chord from the center of the circle and half the length of the chord. We are trying to find the length of the chord, so we need to rearrange the formula to solve for this.

1. For the chord that is 24 cm away from the center:

Let's denote half the length of the chord as a, the distance from the center as b (24 cm), and the radius as c (26 cm). We get the equation:

a² + b² = c² a² + 24² = 26² a² + 576 = 676 a² = 676 - 576 a² = 100 a = √100 a = 10 cm

The length of the chord is twice this, so the length of the chord is 20 cm.

2. For the chord that is 10 cm away from the center:

Again, let's denote half the length of the chord as a, the distance from the center as b (10 cm), and the radius as c (26 cm). We get the equation:

a² + b² = c² a² + 10² = 26² a² + 100 = 676 a² = 676 - 100 a² = 576 a = √576 a = 24 cm

The length of the chord is twice this, so the length of the chord is 48 cm.

So, the lengths of the chords are 20 cm and 48 cm.