Question

The number of diagonals that can be drawn in a polygon of $100$ sides is:

$4850$

$4950$

$9900$

$98$

$8800$

Answer: A

Concepts:diagonal combinations

Difficulty rating: 1410

Small Hint:

Every pair of vertices determines a segment

Big Hint:

Subtract the $100$ sides from the $\binom{100}{2}$ vertex pairs

Solution:

There are $\binom{100}{2}$ segments joining pairs of vertices. Exactly $100$ of these are sides, so the number of diagonals is $\begin{aligned} \binom{100}{2}-100 &=4950-100\\ &=4850. \end{aligned}$

Thus, the correct answer is A.

1950 AMC 12 Problem 45

Answer: A

Difficulty rating: 1410

Small Hint:

Big Hint:

Solution:

Problem 45 in Other Years