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Diagonals of decagon

Posted: Tue Feb 19, 2019 5:22 pm
by samiul_samin
How many intersection point will you get if draw all the diagonal of a $10$ gon?

Re: Diagonals of decagon

Posted: Tue Feb 19, 2019 5:29 pm
by samiul_samin
This is BdMO regional 2016 Question.
Hard way
Draw a $10$ gon
Draw all the diagonals and count the intersection points.
You will get $210$ intersection points.
Screenshot_2019-02-19-17-24-30-1.png
Screenshot_2019-02-19-17-24-30-1.png (126.13 KiB) Viewed 1150 times
This picture is very beautiful to see. :D :D :D
Easy way
We will get an intersection point if we can get $4$ points from $10$ points.
So,answer is $\dbinom {10}{4}=210$