parveen110 wrote:In a convex nonagon all the diagonals are drawn. These diagonals intersect each other at p points inside the nonagon, q points on the nonagon and r points outside the nonagon. Find the maximum possible value of p.
a. 124
b. 96
c. 120
d. 126
OA d
A nonagon is a 9-sided figure.
A diagonal is formed by connecting one vertex to a non-adjacent vertex.
We need to count the total number of interior intersections that can be yielded by these diagonals.
Here, an intersection is formed by means of vertices A, B, C and D.
Here, an intersection is formed by means of vertices C, E, G and I.
Here, an intersection is formed by means of vertices A, E, G and H.
The cases above illustrate that EVERY COMBINATION OF 4 VERTICES can serve to yield exactly ONE INTERSECTION.
Thus, the total number of possible intersections is equal to the total number of ways to choose 4 vertices from 9 options:
9C4 = (9*8*7*6)/(4*3*2*1) = 126.
The correct answer is
D.
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