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?

There are eight equidistant points on a circle. How many right-angled…

Answer

Key fact: By Thales' theorem, any triangle formed with a diameter as one side is a right-angled triangle.
Among 8 equidistant points, each point has exactly one opposite point, so number of diameters = 8/2 = 4.
For each diameter, the third vertex can be any of the remaining 6 points. So triangles per diameter = 6.
Total triangles = 4 x 6 = 24.
Option (a) 24: Correct.
Option (b) 16: Incorrect.
Option (c) 12: Incorrect.
Option (d) 8: Incorrect.
Correction: My earlier conclusion of (d) was a mistake; the counting logic itself gives 24, so the correct answer is (a).