There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?
- 4
- 6
- 8
- 12
Answer
Complete circle makes 360 degrees at the centre.
Each of the 24 equally spaced points subtend an angle at the centre of the circle = 360/24 = 15 degrees
Two consecutive vertices of an equilateral triangle subtend and angle of 120 degrees at the centre.
Number of possible triangles = 120/15
= 8
The correct option is C.