Q.The radius of a circle is 9 cm. Find the length of an arc of this circle which cuts off a chord of length, equal to length of radius.

Step 1: The chord and the two radii $OA=OB=9$ cm form a triangle with all three sides $9$ cm (since chord $=$ radius $=9$ cm), i.e. an equilateral triangle. So the central angle $\theta = 60° = \frac{\pi}{3}$ radian.

Step 2: $s=r\theta = 9\times\frac{\pi}{3}=3\pi$ cm.

Recognise that a chord equal to the radius forms an equilateral triangle with the two radii, giving a 60° central angle, then apply s = rθ.

• Not recognising the equilateral-triangle configuration and instead trying to use the chord-length formula directly for θ.
• Using the chord-length formula chord = 2r sin(θ/2) but then mis-solving for θ.
• Forgetting to convert 60° to radian before applying s = rθ.