# Questions tagged [circles]

For questions concerning circles. A circle is the locus of points in a plane that are at a fixed distance from a fixed point.

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### Relationship between two centers of circles in a Venn diagram

Let $S$ be a circle of 1 unit area. No part of circles $A$ and $B$ are outside the circle $S$. Let $n(S)=1$, $n(A)$, and $n(B)$ be the area of circle $S$, $A$, and $B$, respectively. For the given ...
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### New Proof of Pythagorean Theorem (using inscribed circle)?

I was solving an easy problem for fun when I stumbled onto this, and was wondering if this was a correct and possibly a new proof of the Pythagorean Theorem. Given right triangle $\triangle ABC$, and ...
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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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### Construction involving regular polygons inside a circle

Let's make a construction involving regular polygons: ► First, we begin with a equilateral triangle, with side $\ell_3 = 1;$ ► After, we draw a square on the middle point each side of the initial ...
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### Iterating three tangent circles using Malfatti Circles

First, construct three tangent circles (blue circles), then construct the triangle joining their centers. Then construct three Malfatti Circles for this triangle (green circles). Go on. What I'm ...
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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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### The number of circles that will fit inside the area of larger circle?

Let's say circle $\omega_1$ has a diameter $X$. Let $X>Y$; $Y\in \mathbf{R}^{+}$. How many circles with diameter $Y$ will fit inside $\omega_1$? Is there a formula for this?
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### Is this result already a known theorem in geometry?

I have been playing around with geometry and I found that: Let two perpendicular lines intersect at a point that is inside a circle. Then the area of the quadrilateral formed by the vertices made by ...
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### Right Triangle and Circle Theorem

Let $ABC$ be a triangle such that $\angle BAC$ is a right angle. Suppose $D$ is a point lying on $BC$ such that $BD=1$, $DC =3$ and $\angle ADB=60^{\circ}$, find the length of $AC$. I was told that ...