Mathematics
Mathematics
Problem
In a circle of radius , the length of chord is . What is the distance of the chord from the centre of the circle? a) b) c) d)Intuitive explanation
The key insight is that the perpendicular from the center of a circle to a chord always bisects that chord, creating a right triangle you can solve. Once you drop a perpendicular from the center to the chord, you'll have the radius as the hypotenuse, half the chord length as one leg, and the distance you're looking for as the other leg—then just apply the Pythagorean theorem.
Intuitive explanation
The key insight is that the perpendicular from the center of a circle to a chord always bisects that chord, creating a right triangle you can solve. Once you drop a perpendicular from the center to the chord, you'll have the radius as the hypotenuse, half the chord length as one leg, and the distance you're looking for as the other leg—then just apply the Pythagorean theorem.