Question

There are 24 eqally spaced points lying on 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?

Answer 1

A whole circle = 360 degrees

Each of the 24 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

There are 8 possible triangles that can be made