Tagged Questions

For questions about properties and applications of triangles

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How to parameterize the interior of a triangle

I would like to know how to parameterize a triangle over $[0,1] \times [0,1]$. I actually only care that the mapping is surjective but a bijection is always nice I suppose. I found this in which an ...
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Triangle angle question [closed]

I need help about a triangle angle question.
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How to determine if a triangle is inside another triangle without any intersecting sides

This question is for getting the right logic down for a programming task. I need to be able to determine if a triangle is located inside another without any sides intersecting each other. The two ...
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Distance from Chicago to New York

An airplane flies $520$ miles from Chicago to Virginia. Then it turns $45$ degrees to face New York and flies $630$ miles to New York. What is the distance from Chicago to New York? Given the $45$ ...
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Integer Triangle Radicals conjecture

An integer sided triangle has an area $A$. Heronian triangle areas have no radical, or radical 1. Otherwise, $4 A$ will always be of the form $a\sqrt{r}$, where $r$ is the squarefree radical of the ...
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Is proof of Pythagoras Theorem using Similarity circular?

Please see this link. (hope it doesn't rot) Is this proof circular? I think similarity is proved by basic laws of trigonometry, especially Pythagoras theorem. When I search for proof of Similarity, ...
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How to setup vector story problems

I'm studying for my trig final and I know how to do all the math, but I don't always understand how to setup the story problems. Mostly I'm struggling with vector story problems. For example: Forces ...
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In equilateral triangle,One vertex of a square is at the midpoint of the side, and the two adjacent vertices are on the other two sides of triangle

In the equilateral triangle $ABC,AB=12.$One vertex of a square is at the midpoint of the side $BC$, and the two adjacent vertices are on the other two sides of the triangle.Find the length of the side ...
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Parallelogram -diagonal-similarity problem

Given a parallelogram $ABCD$ . Points $M$ and $N$ are respectively the midpoints of $BC$ and $CD$ . Lengths $AM$ and $AN$ intersecting diagonal $BD$ consecutive points $P$ and $Q$. Prove that ...
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similar triangle problem in parallelogram with vertical lines

Can anyone help me with this task? I have no idea how to start. From the top $B$ of a parallelogram $ABCD$ lowered the vertical $BP$ and $BQ$ on the directions of $AD$ and $CD$ . From the top $D$ ...
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Let $K$ be midpoint of the hypotenuse of a right triangle $ABC$.On the leg $AB$ is a point $M$ s.t $BM=2MC$.Show that $MAB$ and $MKC$ are similar.

Let $K$ be the midpoint of the hypotenuse of a right triangle $\triangle ABC$. On the leg $BC$ is a point $M$ such that $BM = 2MC$ . Prove that the triangles $\triangle MAB$ and $\triangle MKC$ ...
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If the circumcircle of a triangle cuts its nine point circle orthogonally,then prove that $\cos A\cos B\cos C=\frac{-1}{2}$

If the circumcircle of a triangle cuts its nine point circle orthogonally,then prove that $\cos A\cos B\cos C=\frac{-1}{2}$ I know that two intersecting circles are orthogonal if any one of the ...
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Prove $\sin(A-B)/\sin(A+B)=(a^2-b^2)/c^2$ [closed]

prove For any triangle $\triangle ABC$, prove that $$\frac{\sin(A-B)}{\sin(A+B)}=\frac{a^2-b^2}{c^2}$$
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Draw A Triangle From 3 Excenters and Ex-radii

My teacher gave me this problem and told me to think- " Is it possible to draw a triangle, given the three ex-centers and length of the ex-radii?" I don't know if it's possible or not. So, my ...
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Geometry experts! Three equal tangential circles: What is the ratio of the blue line to the red line?

Consider the three tangential circles of equal radii inscribed in the equliateral triangle (linked to below). What is the ratio of the blue line to the red line? The red line is simply the diameter ...
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Prediction Interval from Markov Chains

Thank you for taking the time to look at my question. Short, less involved question: How do you find Prediction Intervals with non-Gaussian residuals? Here is the situation: I have made a model that ...
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Prove that DE || BC

Let M be the midpoint of side BC in triangle ABC. The angle bisector of BMA intersects AB in D, while the angle bisector of CMA intersects AC in E. How can i prove that DE||BC? I drew out the ...