Questions tagged [euclidean-geometry]
For questions on geometry assuming Euclid's parallel postulate.
9 questions from the last 7 days
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Elementary geometry: showing that four points are coplanar
Suppose we are given four coplanar points $A$, $B$, $C$, $D$, in three-dimesional Euclidean space.
Suppose that we are also given four points $A'$, $B'$, $C'$, $D'$, such that $\left| AB \right| = \...
- 31
4
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3
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How to prove that four points are concyclic under these given conditions?
I've stumbled upon the following problem that made me curious for quite a while. Below is one of many possible diagrams of the problem in question.
Given that $ABCD$ is a parallelogram with acute ...
- 429
4
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1
answer
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A question about a pair of triangles in a triangle
An example of this phenomenon.
Given triangle $\triangle{ABC}$, define another triangle $\triangle{A'B'C'}$ such that A' lies on $\overline{BC}$, B' lies on $\overline{AC}$, and C' lies on $\overline{...
- 41
4
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1
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Concyclicity of Fermat points in a cyclic quadrilateral
About six months ago I came up with a nice property related to Ferma points and circular quadrilaterals, but I couldn't prove it:
Let $ABCD$ be a cyclic quadrilateral. For each vertex, consider the ...
- 4,843
3
votes
1
answer
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Existence of this trick-of-the-eye figure in 3-dimensional space
Prove or disprove: There exist eight points $A$, $B$, $C$, $D$, $E$, $F$, $G$, $H$ in $\mathbb R^3$ such that $\square ABCD$, $\square BCGF$, $\square EFGH$ and $\square ADEH$ are convex ...
- 1,860
0
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2
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90
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Non-concyclicity of the circumcenters of complementary triangles in a quadrilateral
About a year ago, I discovered a property related to quatrains, but I haven't been able to prove it. The property is rather strange, and I don't know where to begin proving it. If anyone can help me, ...
- 4,843
4
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How to map square roots as a linear progression on a circle?
I have been exploring geometric constructions with roots. It seems that the fact that the circle is the locus of precise square root dispositions is often overlooked, as I haven't seen it used much in ...
- 483
2
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For three circles, if three paired common tangents concur oddly outside their contact segments, prove the other paired tangents concur too.
For three circles, draw a pair of common tangents for each pair of circles. If the three common tangents in one set are concurrent, and if their point of concurrence lies outside the contact-point ...
- 210
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Is the limiting incenter of a degenerating tetrahedron the Radon point of the four limiting coplanar vertices?
Let $T_n$ be a sequence of nondegenerate tetrahedra in $\mathbb R^3$, with labeled vertices
$$
A_n,B_n,C_n,D_n.
$$
Assume that
$$
A_n\to A,\qquad B_n\to B,\qquad C_n\to C,\qquad D_n\to D,
$$
where $A,...
- 551