# Questions tagged [euclidean-geometry]

Geometry assuming the parallel postulate: in a plane, given a line and a point not on that line, there is exactly one line parallel to the given line through the given point.

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### If we have the slope of $AB$ and $AC$. How can we determine the angle of $AB$ and $AC$?

If we have the slope of $AB$ and $AC$. How can we determine the angle of $AB$ and $AC$? I searched the internet but I don’t understand. Please help! Thank you very much.
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### Given a random point and a cube, how can I determine the distance from that point to the furthest possible point on the cube?

Given a random point in space ( $\vec{p}$ ), I am trying to figure out how to calculate the distance to the furthest point on an axis-aligned cube/cuboid from that other point. This cube is defined by ...
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### Total distinctive nets of regular icosahedron (20-face regular polyhedra)

Came across this on wikipedia: An icosahedron has 43,380 distinct nets. But I can't find the proof to it. Is there an easy to understand proof? Also, if I color the each face of icosahedron with ...
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### Finding the ratio between the area of a circle inscribed by a kite and a circle inscribing the kite

In the following problem, $\angle DAB = 2\alpha$, and $ABCD$ is a kite ($AD=AB, DC=CB$). I need to prove the ratio between the circle inscribed by the kite to the area of the circle inscribing the ...
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### How many points {0,1}^k can a hyper plane in n-dimension contain?

Suppose we have a hyperplane H in $\mathbb{R}^n$ and a set of points S = $\{0,1\}^k,\; k\leq n$. We want to find the maximum number of points that the hyperplane H can contain from the set S. edit: ...
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### Find an angle in the given quadrilateral

In the following problem, I want to find the angle marked as $x$. It seems so simple and yet I am out of ideas. It is very easy to get all angles except two of them: angle ADB and angle CBD. Is ...
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Find the value of $R/r$: I go with co-ordinate geometry, considering the centre of the circles is at the origin, then the equation of the circle becomes as $$x^2 + y^2 = R^2$$ $$x^2 + y^2 = r^2$$...
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### Triangles and inequalities

Let ABC be a triangle and let O be any point in space. How can I show that $AB ^ 2 + BC ^ 2 + CA ^ 2 \leq 3 (OA ^ 2 + OB ^ 2 + OC ^ 2)$? I know this prove by inner products, but is possible to show ...
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### Find the function does describe the the percentage of the area that each circle overlaps

I saw this question, yesterday and it got me thinking, what function does describe the the percentage of the area that each circle overlaps. In that diagram it is given that the distance between the ...
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### Locus of a moving point, when constraints on an angle and length are given

$APQ$ is a variable triangle; $A$ is fixed, $P$ moves on a fixed line $CD$; if $AP$ meets a fixed line parallel to $CD$ at $R$, and if $PQ=AR$ and if the angle $APQ$ is constant, prove that the locus ...
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### Locus of a moving point, such that two distances have a common ratio

A, B are two fixed points on a fixed circle; P is a variable point on the circle; Q is a point on BP, such that BQ/AP is constant; find the locus of Q. The only approach I could think of is through ...
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### Relation between the radius of $n$ identical circles and the radius of an enclosing tangent circle

$n$ small circles are tangent to each other and tangent to the big circle. Here's a figure for $n=4$: Asking hints of how to find the reason between the radius of small circles into the big ...
I would like to find an arbitrary $\mathbf{p} \in \mathbb{R}^3$ point which is not included in any of planes defined by surface normals $\mathbf{s}_1, \mathbf{s}_2,..., \mathbf{s}_m \in \mathbb{R}^3$ (...