# Questions tagged [triangles]

For questions about properties and applications of triangles.

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### Two possible triangle centers.

For every point P in a triangular region T, consider the shortest and longest chords of T that pass thru P. Lets define 'Chord ratio(P)' = ratio between lengths of longest and shortest chords thru P. ...
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### The points A $(0,0)$, B$(\cos(\alpha),\sin(\alpha))$ and C $(\cos(\beta),\sin(\beta))$ are the vertices of a right angled triangle.

$(0,0)$, B$(\cos(\alpha),\sin(\alpha))$ and C $(\cos(\beta),\sin(\beta))$ are the vertices of a right angled triangle. Derive a relation between $\alpha$ and $\beta$." /> I tried using the slope ...
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### How can I prove that two lines intersect at a circle?---an extended observation.

I’m referring to this problem: How can I prove that two lines intersect at a circle?? I decided to graph it on GeoGebra. By accident, I did not draw it correctly. The line $RS$ was not the angle ...
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### Calculate the length of hypotenuse of a right triangle in the complex plane

As the Pythagorean theorem does not work, Base = 1 Altitude = i Hypoteneuse^2 = 1^2 + i^2 = 0? How can this be calculated?
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### Angle dependencies between equilateral and right-angled triangle

Given an equilateral triangle $\triangle ABC$ and a right-angled triangle $\triangle ABD$ where $\angle ADB$ is the right angle and, therefore, the hypotenuse $AB$ is shared with the $\triangle ABC$. ...
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### Usage of similar triangles

This is typically a general question about when we could use similar triangles in real life. Googling this question let me understand that it is very possible to use them for trees, buildings heights ....
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### What is the specific term for an Isosceles triangle where the legs are longer/shorter than the base?

I'm shocked that I couldn't find an answer to this anywhere, but I have a situation where I have to categorize isosceles triangles by whether their legs are (individually) longer or shorter than their ...
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### How to find the coordinates of the vertices of an equilateral triangle inscribed in a given circle?

Let $C = (a, b)$ be any given point in the plane, and let $r$ be any given positive real number. Then how to find the coordinates of the vertices of an equilateral triangle inscribed in the circle  \...
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2 votes
2 answers
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### Understanding a 'geometrical proof' of irrationality of √2

I had been having trouble understanding a proof of the irrational nature of √2. I found this proof in the first page of the foreward to 17 theorem provers of the world where a 'geometrical proof' (is ...
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### Geometry of a diagonal in a flag

Problem I came across the flag of Trinidad and Tobago and it got me thinking about the geometry of that diagonal. Picture below. If you look at the diagonal, you'll see it doesn't just go from one ...
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