Twelve points are located on a circle and C=the number of line segments that can be drawn with these points as endpoints. D = the number of diagonals that can be drawn on a decagon. What is C-D?

Question

mani_jha · Answer

The no. of line segments that can be drawn with those 12 points is C=nC2
The no. of diagonals of a decagon =D= 10C2(no of line segments)-10(no of sides)
Thus C-D=10
Please tell me if u need more help understanding this

anonymous · Answer

i cannot find that answer. please explain again thank you

anonymous · Answer

i do not have that answer on my list. here are the answers i do have:30, 41, 31, 0

mani_jha · Answer

No of line segments = 12C2=66
No of diagonals=10C2-10=35
Thus answer should be 31

anonymous · Answer

I made a mistake. Did not divide by 2! on both sides.

anonymous · Answer

please explain further

mani_jha · Answer

See, if you join any two points on that circle, you get a line segment. So out of 12 points, you can choose any 2. The no of ways in which you can do so is 12C2.
Again, to get a diagonal, you can join any two out of 10 vertices. No. of results will be 10C2. But if you join adjacent vertices, you get a side of the decagon, and not the diagonal.
So, there are 10 sides which shouldnt be counted as diagonals.
So, no of diagonals is 10C2-10
Did u get it?

anonymous · Answer

thank u so much