Question:
Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A,B, C, D, E, F, G, H, J, K, and O so as to form a triangle?
Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A,B, C, D, E, F, G, H, J, K, and O so as to form a triangle?
Updated On: Jul 8, 2025
- 180
- 160
- 170
- 110
Show Solution
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The Correct Option is B
Solution and Explanation
There are 5 pairs of diametrically opposite points and the center O.
If O is not chosen, the number of triangles is \((\frac{10}{3})=120.\)
If O is chosen, the other two points can be selected in \(\frac{10×8}{2}\), i.e., \(40\) ways.
In this case, the number of triangles is \(160.\)
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