There are eight equidistant points on a circle. How many right-angled triangles can be drawn using these point

Question

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?

Accepted Answer

A triangle inscribed in a circle is a right-angled triangle if and only if its hypotenuse is a diameter of the circle. The question explicitly states that the diameter is one side of the triangle, meaning it is the hypotenuse.

1.  Identify the number of unique diameters: With 8 equidistant points on a circle, you can form 8/2 = 4 unique diameters. (Each diameter connects two diametrically opposite points).
2.  For each diameter, consider it as the hypotenuse of a right-angled triangle. The third vertex of the triangle can be any of the remaining points on the circle.
3.  Number of remaining points: There are 8 total points. If two points form a diameter, then 8 - 2 = 6 points remain.
4.  Calculate the total number of right-angled triangles: For each of the 4 diameters, there are 6 possible choices for the third vertex.
    Total triangles = Number of diameters * Number of remaining points = 4 * 6 = 24.

Therefore, 24 right-angled triangles can be drawn.

The final answer is A) 24.

Answer

24

Answer

16

Answer

12

Answer

8

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

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