Try this beautiful Problem on Number theory based on Points on a circle from AMC 10 A, 2010. You may use sequential hints to solve the problem.
Eight points are chosen on a circle, and chords are drawn connecting every pair of points. No three chords intersect in a single point inside the circle. How many triangles with all three vertices in the interior of the circle are created?
,
Number theory
Combination
Circle
Pre College Mathematics
AMC-10A, 2010 Problem-22
$28$
To create a chord we have to nedd two points. Threfore three chords to create a triangle and not intersect at a single point , we have to choose six points.
Now can you finish the problem?
Now the condition is No three chords intersect in a single point inside the circle.Now we know that for any six points we pick, there is only 1 way to connect the points such that a triangle is formed in the circle's interior
Now Can you finish the Problem?
Therefore the required answer is $ 8 \choose 6$=$28$
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