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?

Explanation:

1. Key Principle: A triangle inscribed in a circle with one side as the diameter is always a right-angled triangle, with the right angle at the vertex opposite the diameter.

2. Identify Diameters: With 8 equidistant points on a circle, we can form diameters by connecting opposite points. Since there are 8 points, there are 8/2 = 4 unique diameters. For example, if the points are P1, P2, ..., P8, the diameters would be (P1,P5), (P2,P6), (P3,P7), and (P4,P8).

3. Count Triangles per Diameter: For each diameter, the two endpoints of the diameter form two vertices of the right-angled triangle. The third vertex can be any of the remaining points on the circle. If we pick one diameter (e.g., P1P5), there are 8 total points. We've used 2 points for the diameter. So, there are 8 - 2 = 6 remaining points. Each of these 6 points can serve as the third vertex to form a right-angled triangle with P1P5 as its hypotenuse.

4. Total Triangles: Since there are 4 diameters, and each diameter can form 6 right-angled triangles, the total number of such triangles is 4 diameters * 6 triangles/diameter = 24.

Therefore, 24 right-angled triangles can be drawn.

The final answer is A) 24.