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?

• A. 180
• B. 160
• C. 170
• D. 110

Answer 1

Answer: (B)

160

Answer 2

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 $160.$