Just Another Circle problem!

Calculus Level 5

Compute the average distance between two randomly selected points in a circle(with a radius R = pi). If your answer is a b \frac ab , where a a and b b are coprime positive integers, enter a + b a+b .


The answer is 173.

Rahul Singh by rahul singh , 22, India

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1 solution

The average distance between two points uniformly and independently chosen from a compact convex subset of the s-dimensional Euclidean space.

Paraphrasing closely: Especially, if X is a disc in R 2 \mathbb{R}^2 with diameter d(X), the average Euclidean distance between such points is 64 d ( X ) 45 π \frac{64\,d(X)}{45\,\pi} .

64 × 2 π 45 π ⇒ 128 45 ⇒ 128 + 45 ⇒ 173 \frac{64\times2\pi}{45\pi} \Rightarrow \frac{128}{45} \Rightarrow 128+45 \Rightarrow 173

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