Counting right-angled triangles using diametrically opposed points on a circle

According to Thales's Theorem, any triangle inscribed in a circle with the diameter forming one of its sides is guaranteed to be a right-angled triangle.

First, determine the number of diameters available. Eight equidistant points paired across the center yield exactly 8 / 2 = 4 diameters.

For each unique diameter chosen as the base, you need a third point to complete the triangle. There are 8 - 2 = 6 remaining points on the circumference available for selection. Every single one of these 6 points will form a right-angled triangle when connected to the chosen diameter.

Total triangles = (Number of diameters) × (Available 3rd points) = 4 × 6 = 24.

Answer: (a).