Question

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

Answer 1

Correct Answer - Option 3 : 8

Given:

There are 24 equally spaced points lying on the circumference of a circle

Calculation:

⇒ The complete circle = 360° 

⇒ Each of 24 points subtends an angle at the centre of the circle = 360/24 = 15° 

⇒ Two consecutive vertices of an equilateral triangle an angle of 120° at the center 

⇒ The number of possible equilateral triangle = 120/15 = 8

∴ The required result will be 8.