All Questions
7
questions
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Construction of a pentagon in which an angle bisector at a certain vertex is also a perpendicular bisector of a side opposite to that vertex
Construct a pentagon $ABCDE$ if lengths of its sides are $a,b,c,d$ and $e$ ($|AB|=a,|BC|=b,...$), and the bisector of the angle at vertex $D$ is also the perpendicular bisector of $AB$.
I know that $...
- 429
2
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1
answer
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Given a quadrilateral with 4 equal areas, prove that it is a parallelogram
I have the next quadrilateral with midpoints E F G H. The source of the problem is my class of geometry, I read the book but I don't find anything related to this.
I found in Google about Varignon's ...
1
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1
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Constructing an isosceles trapezoid with a specific decomposition into triangles
A recent question asked about finding the ratio of the bases for the following isosceles trapezoid:
That problem has been solved, obtaining a result of $|CD|/|AB|=1-1/\sqrt{2}$. What I'm curious how ...
- 16.8k
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1
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Given a Pentagon, Construct a Parallelogram Equal in Area
Euclid claims in I.45 of his Elements to show how to "construct a parallelogram equal to a given rectilinear figure in a given rectilinear angle." In modern terms, he is saying that he will show how ...
- 199
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1
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A Robbins Pentagon bound to any (non-isosceles) Integer Triangle?
Given any non-isosceles triangle $\triangle ABC$, and denoting $AB$ its longest side, the following construction
determines the points $DFGE$ (see this post for details).
My conjecture is that if ...
user559615
2
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5
answers
334
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Where is the hole in this argument asserting the constructibility of all regular polygons?
Some engineers have a so-called "general" method for constructing any (regular) polygon with the classical instruments only, given the length of its side (they may recognise that it appears to be ...
- 13.4k
2
votes
1
answer
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Constructing hexagon from nine lengths
This question made me think: suppose you have an irregular hexagon $ABCDEF$, and you know the edge lengths $AB,BC,CD,DE,EF,FA$ as well as the diagonal lengths $AD,BE,CF$. Then counting degrees of ...
- 43k