Questions tagged [circles]
For elementary questions concerning circles (or disks). A circle is the locus of points in a plane that are at a fixed distance from a fixed point. Use this tag alongside [geometry], [Euclidean geometry], or something similar. Do not use this tag for more advanced topics, such as complex analysis or topology.
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How do you find the intersection between 2 complex shapes?
One thing I've done to find if two perfect circles intersect is to compare the radii of both circles to the distance between them, which isn't complicated at all. However, for non-circle shapes, I don'...
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For what values of $n$ can coins of radius $\frac12,\frac13,\frac14,...,\frac1n$ be held rigidly in a circular tray of radius $1$?
For what values of $n$ can circular coins of radius $\frac12,\frac13,\frac14,...,\frac1n$ (at least one of each, and no other kind of coin) be held rigidly in a circular tray of radius $1$?
By "...
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How can I convert Interval Difference to Circle of Fifths segments and position
How to convert Interval Difference to Circle of Fifths segments and position
Hi, Im designing a numeric decimal notation code model for exploring math relations between notes on chromatic scales and ...
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Geometry question about a six-pack of beer
On a hot summer day like today, I like to put a six-pack of beer in my cooler and enjoy some cold ones outdoors.
My cooler is in the shape of a cylinder. When I place the six-pack in the cooler ...
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Sangaku problem involving eight circles
I made the following sangaku problem.
$\dfrac{\text{Area of the orange circle}}{\text{Area of a blue circle}}=\space ?$
Description of diagram. In this question, circles of the same color are ...
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What is the maximum area of n non-overlapping equal area triangles inscribed in a circle of radius
What is the maximum area of n non-overlapping equal area triangles inscribed in a circle of radius 1?
For n = 1, the triangle is equilateral.
For n = 2, we have 2 isosceles right triangles sharing a ...
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If I have x and y coordinates of a point along the arc, how do I convert that to a percentage of PI?
I am using Javascript to create shapes in canvas. I am creating an arc where you specify the start and end angle of the arc to show where along a circle the arc begins and ends. They are initially set ...
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Proving Symmedian intersects intersection of tangents
I'm going through Evan Chen's "Euclidean Geometry in Math Olympiads" and I've come to Chapter 4's section on Symmedians.
Proposition 4.24 says:
Let $X$ be the intersection of the tangents to ...
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Solving Tangent Circles, Lines, and the Angles Between Them [closed]
As shown in the picture, I have two smaller diameter circles of a known diameter, d. I have a single larger circle of unknown diameter, D. And two lines (or one), each tangent to both one of the ...
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Lattice points inside $x^2+y^2=r^2$
In the interior of the square of side length $N$, whose two corners are lattice points $(m,m)\in\Bbb Z^2$, there are $(N-1)^2$ lattice points.
So, in the intetior of the circle $$x^2+y^2=r^2,\,\, r\in\...
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The unit disc contains finitely many dyadic squares whose total area is arbitrarily close to the area of the disc
Exercise 1.25.a in Pugh’s Real Mathematical Analysis states that
Given $\epsilon > 0$, show that the unit disc contains finitely many dyadic squares whose total area exceeds $\pi - \epsilon$, and ...
user1327236
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A beautiful property that connects five points located on a circle to the nine point circles
A while ago, while playing with the GeoGebra program, I came across a distinct geometric property, and I would like to know whether it has been previously discovered or not, and also how this complex ...
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Is there a geometrical diagram in which it is evident that two circles' radii have ratio $1:11$?
There are geometrical diagrams in which it is evident* (to a skilled geometer) that two circles' radii have a certain integer ratio.
For example, for the following diagram, it is evident that the ...
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Prove that the tangents from point $A$ and the tangent from point $B$ to the circle $k_1$ are parallel.
Given is a circle $k$ with diameter $AB$. On it, we choose a point $M$, which is not coincident with $A$ or $B$. Let $k_1$ be the circle that has its center at $M$ and is tangent to the diameter $AB$. ...
user1315539
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Find the segment BT in the triangle inscribed below
In the figure, $AB.BC = 60$ and $BT.TP = 40$.
Calculate BT with B and T tangency points.
(Answer:$2\sqrt5$)
I try:
$AT.TC = BT.TP \implies AT.TC = 40$
$AM.AB = AT.AC$
$AT^2 = AM.AB \implies AT^2 = AT....
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