Questions tagged [geometry]
For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, and angles.
52,609 questions
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A straightforward proof of a property of lines enveloping an ellipse using complex numbers : looking for connections
This question finds its origin in the very fruitful exchange I have had with @Li Kwok Keung, in the framework of this question.
Let us consider the following plane geometrical configuration that I ...
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Identify the flaw in my proof [closed]
they said I had to find AE,the actual answer is 64/11 but I have the answer at 6,my math teachers said i was correct since they could nt find any errors with my proof
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similar to a classical geometry result
Let $\triangle ABC$ be a triangle and $O$ its circumcenter.
We define $f(\triangle ABC) = \triangle A'B'C'$ such that $A',B',C'$ are the circumcenters of the triangles $\triangle OBC,\triangle OCA, \...
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How to prove that $n=7$
On the line $d$ we consider the points
$A_1, A_2, \ldots, A_{15}$, all distinct two by two, such that
$
A_1A_2 = A_2A_3 = \cdots = A_{14}A_{15} = 1.$
Find the smallest natural number $n \ge 4$ with ...
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Is there something missing with this simple geometry problem?
I'm currently doing an exercise form my geometry book. The question is asking for the volume of the pyramid $N.ABCD$ (i.e. a pyramid of base $ABCD$ and with the tip $N$). The construction is as ...
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Semicircle with tangent and perpendicular: prove that DE·BC = CD·R [closed]
Problem
Given a semicircle with diameter AB = 2R and center O. Let C be a point on the
extension of AB beyond B. From C, draw a tangent CD to the semicircle, touching
it at point D. The perpendicular ...
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Explain this seeming contradiction in Euclid Book 1 Proposition 16
This proposition has been concluded without the use of the parallel postulate, because the first time Euclid invokes the parallel postulate is in I.27. Thus, it should apply to all geometries ...
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Given an $n$-gon, by how much must we increase the length of each of $k$ chosen sides so that they form a $k$-gon?
The polygon inequality states that the sum of any $n-1$ sides of a $n$-gon greater than the $n$-th side.
Let $n \ge 4$ and $3 \le k < n$. Let a $n$-gon have positive side lengths $
a_1 \le a_2 \le \...
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if AB and AC are two tangents to a circle and ∠BAC = 116°, find the magnitudes of the angles in the two segments into which BC divides the circle. [closed]
I don't really understand what does the statement 'find the magnitudes of the angles in the two segments in which BC divides the circle' mean.'
Do I need to add a new tangent in order to create and ...
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Radium Rabbit Conjecture, version 3.0: The fractional part of the square of the area of a triangle with odd-integer sides is $\frac{3}{16}$. [closed]
Why Version 3.0?
In the earlier versions of this conjecture, I focused on triangles whose side lengths are distinct prime numbers.
Through the discussion that followed, it became clear that the ...
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Hot take on the "Coastline Paradox" [closed]
Edit:guys I don't mean to disrupt, I am really just an amateur and I would really appreciate if you let me know why I'm wrong or if I'm right
Note: this is just my view of the coastline paradox, if ...
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Can four points in a unit square have mutual distances all larger than 1?
Question: 4 points are given inside or on the boundary of a unit square. I have a conjecture that there must be 2 points at a distance $\leq 1$.
Progress: I’ve found that this question is a corollary ...
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Six circles in a rectangle: show that two lengths are equal
The diagram shows a rectangle, six circles, and a red line segment joining the centres of two circles. Wherever things look tangent, they are tangent. (The tangencies imply that there are three pairs ...
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Inscribed equilateral triangle side [closed]
In the picture there are two small circles with centers B and C, crossing at D, whose center lie on top of the large circumference.
I know that line AB is the side of an equilateral triangle, and that ...
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How is he triangle spanned by $z_1, z_2, z_3$ is given by $ z=t_1 z_1+t_2 z_2+t_3 z_3, 0 \leq t_1, t_2, t_3, t_1+t_2+t_3=1$?
In my complex analysis book:
Let $z_1, z_2, z_3 \in \mathbb{C}$ be three points in the complex plane. The triangle spanned by $z_1, z_2, z_3$ is the point set
$$
\Delta:=\left\{z \in \mathbb{C} ; \...
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