Questions tagged [geometry]
For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, and angles.
52,596 questions
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Triangle with equidistant centers.
Consider $\triangle ABC$ and let $H$, $I$, $O$ be its orthocenter, incenter and circumcenter respectively. Show that:
$$OH \geq OI$$
$$OH \geq HI$$
I stumbled on this properties while experimenting ...
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Find a synthetic proof to an old problem .
I found this problem in a French paper translated from Arabic in 1927 by an author named Al Bayrouni . I wonder if it can be found in one of Archimedes' works . Here is the statement :
ABC is a ...
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Proving hermite conditions of a polygonal patch
In parametric lines, constructing the standard hermite basis is trivial.
We have two points $p_1, p_2$ and two tangent vectors $t_1, t_2$. Thus we have 4 unknowns that will be sampled, for that we ...
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Is my Euclidean-style proof valid? It is for a summation of infinitely many line segments equaling to a finite length without calculus, or limits. [closed]
I have attempted to prove that the sum of infinitely many quanities can still equal a finite quantity without using calculus, measure theory, or any other modern mathematical tool such as set theory.
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Basic Proportionality Theorem/ Thales Theorem [closed]
The Basic Proportionality Theorem seems so obvious but the construction to prove it (drooping perpendicular to equate areas) is not at all obvious to me. Can anyone tell how to prove this Theorem in a ...
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geometric problem for spiral similarity
We consider a quadrilateral $ABCD$ inscribed in a circle $\omega$. Let $P$ be a point inside $\omega$ and the following equalities are satisfied
$$\angle PAD = \angle PCB,\ \angle ADP = \angle CBP.$$ ...
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Find out the distance between centers of two intersecting semi-ellipses $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$.
There are two identical semi-ellipses, one with center at the origin $O$, $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, and the other at $R$, $\frac{(x-d)^2}{a^2}+\frac{y^2}{b^2}=1$.
Find out the distance $d$ ...
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Is this a known theorem?
Reference image ^^^
Edit: a person has answered this and I have rediscovered Euclid's Elements, Book 13, Proposition 15.
Ok so I think I might have found a new theorem or maybe rediscovered an old one....
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How would you determine a circle diameter using three smaller known circle diameters that all fit neatly within this circle. [closed]
Given three circles with diameters of .623", .687", and .719" that fit snugly within a circle of diameter D, what is D? What is the mathematical formula for this?
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Find the value of y in this geometric figure
Find the value of $y$ in the following geometric figure, as a function of $v_1$, $v_2$, $x$ and $H$. All angles that visually seem to be $90°$, are.
I was asked to share what I tried, so here it goes....
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What is the measure of the angle between the two diagonals of this trapezoid?
The attached figure represents a trapezoid ABCD with four angles indicated.
My objective is to calculate the angle x formed by the two diagonals AC and BD.
Using GeoGebra, I found that x is almost 106°...
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A subset of a rectangle that 'blocks' every curve that goes from right to left must connect upper and lower sides
I'm trying to find a proof for the following assetion: Given a rectangular region $R$ and a subset $A$ of $R$, if every curve that starts at the left side of $R$ and ends at the right side intersects $...
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How to find the maximum length of chord cut by a right angle inside a circle
How to find the maximum length of chord AB in the figure below?
P is a fixed point inside circle centered at O (P is not O). PA and PB form a right angle. Imagine this right angle rotates inside the ...
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Over $\mathbb R^2$, given a tool that can $n$-sect an angle for any $n$, for which $n$ can you construct the $n$th root of any given $x > 0$?
It's classically known that you cannot, say, construct the $n$th root of $2$ for $n \ge 3$ and $n$ not a power of $2$ with just ruler and compass. However, recall taking $n$th roots and the Chebyshev ...
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Exercise in Acoustic Doppler Effect
I am looking for some guidance on the second part of a geometry type problem which I have given working on and described the next parts below (likely with an error). I have given multiple attempts but ...
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