Geometry L1

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?

  1. 4
  2. 6
  3. 8
  4. 12


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.