If $12$ distinct points are placed on the circumference of a circle and all the chords connecting these points are drawn, at how many points do the chords intersect? Assume that no three chords intersect at the same point.
I tried drawing a circle and tried to find a pattern but couldn't succeed. for 12 points I found the answer to be $(1+2+....+9)+(1+2+3+.....+8)+....+(1)$ and the result multiplied by $2$. But I'm getting $296$ which is in none of the options. Can anyone help?