# Tagged Questions

For questions conserning circles. A circle is a curve composed of points in a plane that are at a fixed distance from a fixed point.

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### What's the average distance between two discs in the plane?

Consider two discs in the plane of radius $r$ and $s$, with centers separated by a distance $l$. If we choose a point uniformly at random from each disc, what is the expected distance between the two ...
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### Stacking circles

When I tried to stack 21 circles of radii $(30, 31, 32... 50)$ on top of each other in a tube (ID of $100$ wide), I thought they would reach the same height regardless of the order, however I was ...
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### Pinwheel- perimeter of semicircular region

Above, we have a larger circle of $r=16$ with 8 equally spaced semicircles of radius=8. Each semicircle has one end on the larger circle's center and the other on the circumference of the larger ...
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### Archimedes Classic Proof for Area of Circle: Love it but can't grasp one aspect…

The proof assumes that:... The perimeter of any CIRCUMSCRIBED regular polygon is GREATER than the circumference of the circle. ie: !http://www.themathpage.com/atrig/Trig_IMG/eval1.gif Is this an ...
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### Prove that the circle contains the polygon.

Given a convex polygon. The circle is constructed for every triple of consecutive vertices of the polygon.We get the n circles. Select the circle with the largest radius. Prove that the circle ...
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### The reverse pizza problem .

The pizza problem is a fairly well-known problem which sounds like this : You have a circular pizza and you need to cut it such that you and your friend would both receive half of the pizza . ...
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### Find circles that completely cover a polygon minimizing the amount of space covered outside the polygon

I have an arbitrary polygon that I need to roughly represent using circles. Any point inside the polygon must lie inside a circle. There will be points outside the polygon that will fall under a ...
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### Why does (h,k) generally represent the center of a circle?

Why are h and k generally used to denote the coordinates of the center of a circle? After a bit of research, we found that h may represent "horizontal shift" or "horizontal translation", but we're ...
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### Centroid and circumcenter — how close?

Suppose $R$ is some planar region, bounded by a curve. Let $C_1$ be the centroid of $R$, and let $C_2$ be the center of the "circumcircle" (the smallest circle enclosing $R$). Intuitively, it seems ...
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### A question concerning radians and arc length

I was asked by a colleague yesterday about how the formula for the arc length of a circle is derived. I wanted to give them a correct answer, so I said I'd get back to them once I'd thought about it ...
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In cyclic quadrilateral ABCD, let E, F, G, H be the orthocenters of triangles BCD, CDA, DAB, ABC, respectively. Prove that EFGH is cyclic. Progress So far, found that if E is orthocenter of BCD ...
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### Finding locus of circle passing through extremities of the two rods

Two thin rods AB and CD of length 2a and 2b moves along OX and OY where O is the origin. Find the locus of the center of the circle passing through the extremities of the two rods. My attempt:- ...
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### Circle continuty principle proof

Circular continuity principle: If a circle C has one point inside and one point outside another circle C' , then the two circles intersect in two distinct points. I read this on Euclidean and ...
The task is to express the length of an arc of a circle trapped between two radii named $r$ if the angle between them is infinitesimally small, named $d\theta$. The solution to this problem is ...