1950 AMC 12 Problem 45

Question

The number of diagonals that can be drawn in a polygon of

100

sides is:

4850

4950

9900

98

8800

Every pair of vertices determines a segment

Subtract the

100

sides from the

\binom{100}{2}

vertex pairs

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.

Problem 45 in other years