Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 13 cm.

Calculations:

The radius of the circle, r = 13 cm, and the perpendicular distance from the center of circle to the chord, d = 5 cm.

The length of the chord can be found using the Pythagorean theorem:

l = 2 ×  √(r² - d²)
Substituting the given values into the formula, we get:

l = 2 ×  √((13)² - (5)²)
l = 2 × √(169 - 25)
l = 2 × √(144)
l = 2 × 12
l = 24 cm
So, the length of the chord is 24 cm.