There are eight equidistant points on a circle. How many right-angled triangles can be drawn using these…
There are eight equidistant points on a circle. How many right-angled triangles can be drawn using these points as vertices and taking the diameter as one side of the triangle?
24
16
12
8
Solution
With 8 equidistant points there are 4 diameters. For each diameter, the right angle vertex can be any of the remaining 6 points, giving 6 right-angled triangles per diameter. Total = $4 \times 6 = 24$.