Questions tagged [euclidean-geometry]
For questions on geometry assuming Euclid's parallel postulate.
10,047 questions
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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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What if we established a relationship between the circumference of a circle and the circumference of its inset square to demonstrate the truth of π? [closed]
The relationship between the circumference of a circle and the circumference of its inner square:
I drew a circle with a diameter d = 1 cm and a radius r = 0.5 cm. Therefore, the circumference of the ...
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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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Draw an isosceles triangle equal in area to a triangle ABC, and having its vertical angle equal to the angle A
I am trying to solve the question
Draw an isosceles triangle equal in area to a triangle ABC, and having its vertical angle equal to the angle A.
I have tried to approach the problem from backwards (...
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Prove that triangle BNC is isosceles in a 30-60-90 construction
Given a right triangle $ABC$ with $\angle A=90°$ and $\angle B=30°$. On the extension of side $CA$, we take point $D$ such that $AD=AC/2$, and on the interior of side $BC$, we take point $E$ such that ...
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Find Angle Without Using Trigonometry
Let $ABC$ be an isosceles triangle with $AB = AC$ and $\angle BAC = 108^\circ$. A point $M$ lies inside triangle $ABC$ such that
$$
\angle MAB = 30^\circ \qquad \text{and} \qquad \angle MBA = 12^\circ....
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Minimizing perimeter with fixed area
Problem: Wasim has $6$ poles and a huge rope. He was asked to occupy a
plot of land measuring $96\sqrt{3}$ square meters in the middle of a
very large field. In order to occupy the land, Wasim has to ...
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What is the nature of a triangle for which the square of the diameter of its circumcircle is equal to the sum of the squares of two of its sides?
Fifty years ago , when I was in college, our teacher , Mrs Marie -Jo , gave us this homework assignment for the holidays :
" Find the two types of triangles such that the square of the diameter ...
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Does the Radical Axis of the Circumcircle and the Miquel Circle of a Cyclic Quadrilateral Coincide with the Steiner Line?
A few months ago, while experimenting with GeoGebra, I came across what looks like an interesting property:
In a cyclic quadrilateral, the radical axis of the circle through the four vertices and the ...
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Help Revising a 2-Column Proof for Euclid's Elements I.7
This is my working 2-column proof for Book 1 Proposition 7. I would be remiss in saying that this is completely foolproof. One question is how we are to formulate a proof by contradiction within the ...
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Struggling with geometry for weird reasons. [closed]
I have this book I'm trying to be good at : Stanford problems.
I do well or good enough at problems involving only numbers but I can't do the geometry problems for the life of me. Not even after ...
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Triangle with equidistant centers.
Consider $\triangle ABC$ and let $H$, $I$, $O$ be its orthocenter, incenter and circumcenter respectively. Show that:
$$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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