Semicircles this time

Probability Level pending

The figure above depicts 5 equally spaced points (A,B,C,D and E). Calculate the number of semicircles in this figure.


The answer is 20.

Ashish Menon by Ashish Menon , 20, India

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1 solution

Ashish Menon
Apr 16, 2016

On the upper part of line segment AE, number of semicircles = ∑ n = 1 4 n = 4 × 5 2 = 10 \displaystyle \sum_{n=1}^{4} n = \dfrac{4×5}{2} = 10
Similarly, on the lower part of line segment AE, number of semicircles = ∑ n = 1 4 n = 4 × 5 2 = 10 \displaystyle \sum_{n=1}^{4} n = \dfrac{4×5}{2} = 10

∴ \therefore The total number of semicircles = 10 + 10 = 20 10 + 10 = \boxed{20}

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