How many chords can be drawn through 5 points on a circle?

The correct answer is Option (2) → 10

A chord joins two points of the circle, and joining P to Q gives the same chord as joining Q to P. So the number of chords is the number of ways of choosing 2 of the 5 points, order not counted.

• \(\displaystyle^{5}C_2=\frac{5\times4}{2}=10\)

Tip: No three points on a circle lie on one straight line, so every pair gives a different chord: \(n\) points on a circle give \(\displaystyle\frac{n(n-1)}{2}\) chords.