# Questions tagged [triangles]

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### Determine cartesian coordinates of these points

Let $ABCD$ form a quadrilateral where $A$ is adjacent to $D$. $A$ has coordinates $(0,0), B$ has coordinates $(1,0)$. Let $ABFG$ form a parallelogram. $F$ has coordinates $(x_F,y_F)$ and $G$ has ...
121 views

### Triangle centers formed a rectangle associated with a convex cyclic quadrilateral

Similarly Japanese theorem for cyclic quadrilaterals, Napoleon theorem, Thébault's theorem, I found a result as follows and I am looking for a proof that: Let $ABCD$ be a convex cyclic quadrilateral. ...
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1 vote
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### Name of the perspector of the orthic triangle and excentral triangle

The orthic triangle and tangential triangles of a given triangle are in perspective. What's the official kimberling center associated with this perspector?
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### Name this kimberling center

The lines which connect the vertices of a triangle with the tangent points between the Spieker circle and the medial triangle are concurrent. Which kimberling center does this point correspond to?
1 vote
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### A circle is inscribed in a triangle, with three other circles in the corner regions. The radii are integers. Possible values of the largest radius?

Originally posted at MSE. A circle with integer radius $R$ is inscribed in a triangle. Three other circles with integer radii $a,b,c$ are each tangent to the large circle and two sides of the ...
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1 vote
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### An "almost" geodesic dome

A regular $n$-gon is inscribed in the unit circle centered in $0$. We want to build an "almost" geodesic dome upon it this way: on each side of the $n$-gon we build an equilateral triangle ...
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### The vertices of a triangle are three random points on a unit circle. The side lengths are, in random order, $a,b,c$. Show that $P(ab>c)=\frac12$

The vertices of a triangle are three unifomly random points on a unit circle. The side lengths are, in random order, $a,b,c$. There is a convoluted proof that $P(ab>c)=\frac12$. But since the ...
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### Packing an upwards equilateral triangle efficiently by downwards equilateral triangles

Consider the problem of packing an upwards-pointing unit equilateral triangle "efficiently" by downwards-pointing equilateral triangles, where "efficiently" means that there is ...
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### Another variant of the Malfatti problem

We try to add to A Variant of the Malfatti Problem As stated in the Wikipedia entry on Malfatti circles, it is an open problem to decide, given a number $n$ and any triangle, whether a greedy method ...
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### Is there a pyramid with all four faces being right triangles? [closed]

If such a pyramid exists, could someone provide the coordinates of its vertices?
1 vote
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### Partitioning polygons into obtuse isosceles triangles

Ref: Partitioning polygons into acute isosceles triangles Partition of polygons into 'strongly acute' and 'strongly obtuse' triangles https://math.stackexchange.com/questions/1052063/...
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1 vote
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### Cutting off odd numbers of equal area triangles from a unit square

Two earlier related posts: Cutting the unit square into pieces with rational length sides On a possible variant of Monsky's theorem Question: for odd n, how does one cut the unit square into n ...
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1 vote
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### Tiling the plane with pair-wise non-congruent and mutually similar triangles

Question: Is it possible to tile the plane with triangles that are (1) mutually similar, (2) pairwise non-congruent and (3)non-right? No other constraints. Note 1: Reg requirement 3 above: since any ...
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1 vote
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### How many convex polygons can be made from $n$ identical right angle triangles?

Whilst working on a Tangram problem, I came across the need to find the total number of convex shapes that can be produced from $16$ identical (isosceles) right angle triangles (since the Tangram can ...
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### Do the heights of an acute triangle intersect at a single point (in neutral geometry)?

A well-known result of the Euclidean planimetry says that the heights of any triangle have a common point called the orthocentre of the triangle. This result is not true in neutral geometry (i.e., ...
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### The 4th vertex of a triangle?

I was immensely surprised and amused by the idea of the fourth side of a triangle that was introduced by B.F.Sherman in 1993. 'Sherman's Fourth Side of a Triangle' by Paul Yiu is available here. ...
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### Constructing an equilateral triangle using Tarski's axioms for geometry

In Euclid's first geometry proposition, he constructs an equilateral triangle given an arbitrary line segment. I was wondering if it was possible to prove this straight from Tarski's axioms for ...
284 views

### Need help with finding all angles of 11 sided 3D object [closed]

Question: I'm an artist trying to build a hendecahedron for a project (Image below to see the shape). This object consists of 5 pentagons at the base, 1 pentagon on the bottom, then 5 quadrilaterals ...
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### Three circles intersecting at one point

Can you provide a proof for the following proposition: Proposition. Let $\triangle ABC$ be an arbitrary triangle with nine-point center $N$ and circumcenter $O$. Let $A',B',C'$ be a reflection points ...
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