1998 CEMC Gauss (Grade 7) Problems/Problem 21

Problem

Ten points are spaced equally around a circle. How many different chords can be formed by joining any 2 of these points? (A chord is a straight line joining two points on the circumference of a circle.)

$\text{(A)}\ 9 \qquad \text{(B)}\ 45 \qquad \text{(C)}\ 17 \qquad \text{(D)}\ 66 \qquad \text{(E)}\ 55$

Solution

From each point, there are 9 other points that you could link it to. However, this accounts for each chord twice, so the answer is $\frac{9 \cdot 10}{2} = 45,$ or $\text{(B)}.$

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1998 CEMC Gauss (Grade 7) Problems/Problem 21

Problem

Solution