# Tagged Questions

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### Placing a circle in a square lattice

Two part question. Consider the square lattice $\mathbb{Z}^2$: Imagine you are going to place a circle of radius $r$ somewhere in $\mathbb{R}^2$. Question 1: What is the radius of the largest ...
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### fixed length random chord outside of circle.

consider a uniform distribution on a unit circle, I construct a cord by the following steps: pick one endpoint A within the unit circle uniformly. points that are $0<d<1$ distance away from ...
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### Expected number of points on circle to form an acute angled triangle

This problem was asked to me in an interview. We keep on adding points on a circle uniformly until there exist three points on the circle which form an acute angled triangle. What is the expected ...
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### What is the probability that the center of the circle is contained within the triangle?

Consider the triangle formed by randomly distributing three points on a circle. What is the probability of the center of the circle be contained within the triangle?
If $N$ points on the circumference of a circle are chosen at random, what is the probability $F(\theta)$ that the maximum gap between neighboring points is at least $\theta$? Because the gaps sum to ...