For questions about triangles

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10
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3answers
166 views

For which n are there primitive Pythagorean triples with legs of lengths a and a+n?

For which n can $a^{2}+(a+n)^{2}=c^{2}$ be solved, where $a,b,c,n$ are positive integers? I have found solutions for $n=1,7,17,23,31,41,47,79,89$ and for multiples of $7,17,23$... Are there ...
1
vote
1answer
374 views

A plane Geometry Problem

The triangle $ABC$ has $CA=CB$, circumcenter $O$ and incenter $I$. The point $D$ on $BC$ is such that $DO$ is perpendicular $BI$. Show that $DI$ is parallel to $AC$.
0
votes
2answers
126 views

Question on Triangles

In a right triangle, the length of hypotenuse is $c$. The centers of three circles of radius $c/5$ are found at its vertices. Find the radius of the fourth circle which touches the three given ...
0
votes
2answers
1k views

Calculate surface normal of each equilateral triangle in a tetrahedron

How can I calculate the surface normal of each equilateral triangle that makes up a tetrahedron? These are the xyz coordinates of the tetrahedron (+1, +1, +1) (−1, −1, +1) (−1, +1, −1) (+1, −1, −1)
1
vote
4answers
182 views

Inverse triangle equality [duplicate]

Possible Duplicate: Why exactly can you take the absolute value of one side of this inequality and assume it is still true? Why is $||a|-|b|| \ge |a|-|b|$, tried a lot (like comparing to ...
0
votes
1answer
161 views

What is the ratio of the area?

If the segment A'B' is tangent to the incircle of triangle ABC, and that segment AB = segment CM; then, what is the ratio of the area of the triangle ABC to the area of the small triangle A'B’C? ...
1
vote
2answers
122 views

What is the area of triangle AFE?

If ED = 23 , and the value of the side of the square ABCD is a multiple of 11, what is the area of the red triangle AFE?! Find the very shortest way to solve this puzzle and use only basic geometry, ...
1
vote
2answers
5k views

How to find the third coordinate of a right triangle given 2 coordinates and lengths of each side

p2 |\ |b\ | \ A| \C | \ |c___a\ p1 B p3 If given point p1 & p2, side A & B how would you find point p3? I know given this information you ...
1
vote
2answers
130 views

Is there a solid where all triangles on the surface are isosceles?

Are there any solids in $R^{3}$ for which, for any 3 points chosen on the surface, at least two of the lengths of the shortest curves which can be drawn on the surface to connect pairs of them are ...
4
votes
2answers
424 views

Proving $\cot(A)\cot(B)+\cot(B)\cot(C)+\cot(C)\cot(A)=1$

I was stumped by another past-year question: In $\triangle ABC$, prove that $$\cot(A)\cot(B)+\cot(B)\cot(C)+\cot(C)\cot(A)=1.$$ Here's what I have done so far: I tried to replace $C$, using ...
3
votes
1answer
84 views

Name for this triangle centre

Given a triangle I draw circles around each vertex. I chose the radii of these circles so that they are all mutually tangent. There is only one way to do this. I extend these tangents. They concur at ...
2
votes
1answer
2k views

calculating the Fermat point of a triangle

Is there any algorithm by which one can calculate the fermat's point for a set of 3 points in a triangle? a fermat's point is such a point that the sum of distances of the vertices of the triangle to ...
3
votes
2answers
189 views

How do I prove that the following method to find whether a point lies within a polygon is correct?

I came across the following method to determine whether a given point lies inside a convex polygon - however, I'm not sure how to prove it. Given any three points on the plane $(x_0,y_0)$, ...
8
votes
3answers
543 views

Sliver triangle

Reading through geometric algorithms and code, I've encountered a term I'm not familiar with, and even the mighty google has not been that helpful: What is a sliver triangle ? From what i ...
1
vote
1answer
92 views

Triangle geometry - lines that separate in two parts of equal area

Consider the set of lines that separate a triangle in two parts of same area. The three median belong to the set, in particular. What can be said of the envelope of the set of lines? For example, is ...
2
votes
2answers
842 views

Ratio of angle division by a line drawn in Triangle?

If a line drawn from one point of a triangle divides opposite side in ratio 1:2 then in what ratio angle is divided by line?
3
votes
2answers
187 views

Testing Whether a Vertical Line Intersects a Plane

Okay, so, I'm not the greatest with geometry (I actually need this for game development), but basically, I need to be able to test whether a vertical (the y-axis is my vertical axis for this) line ...
2
votes
4answers
803 views

Given a triangle with two known vertices and the angle, get the coordinates of the last vertex

I have tried attaching an image of the triangle I am working with but since I am a new user this site will not let me post images (kind of defeats the purpose, but anyways). I have the following ...
0
votes
0answers
222 views

problem finding a 2D Point in a triangle

I have a Triangle with 3 Points - A, B and C and the angle alpha A and B are fixed. C is any point at the side of 'b' Alpha has at A and B the same size I need to find any Point on side 'a' except B ...
2
votes
4answers
531 views

Geometry/ Similar Triangles Problem

Consider the trangle shown below with vertices A, B, C where point D lies on the side AB, point E lies on the side BC and point F lies on the side AC and the three lines AE, BF, and CD intersect at a ...
0
votes
2answers
1k views

How do I map a 3D triangle into 2D?

The problem I'm having is mapping a 3D triangle into 2 dimensions. I have three points in x,y,z form, and want to map them onto the plane described by the normal of the triangle, such that I end up ...
1
vote
3answers
7k views

How to find triangle height?

I need to know the height (h) of a triangle with two unknown angles (alpha and beta) and the known length of two sides AB and BC. Is it possible to have that value of h (height)?
6
votes
2answers
220 views

Similarity of Triangle problem

Given: AD & PS are medians in ΔABC and ΔPQR respectively, $$\frac{AB}{PQ}=\frac{AD}{PS}=\frac{AC}{PR}$$ To Prove: ΔABC ~ ΔPQR Figure: Problem: In ΔABD & ΔPQS or in ΔADC & ΔPSR or ...
0
votes
1answer
129 views

Creating random triangles with points on the radius of a sphere and passing through center

I'm trying to create a pointy "ball" in 3d space using triangles. I want each triangle to pass through a sphere's center, with each point lying on the surface. I can easily make points on the ...
16
votes
3answers
2k views

Proving Stewart's theorem without trig

Stewart's theorem states that in the triangle shown below, $$ b^2 m + c^2 n = a (d^2 + mn). $$ Is there any good way to prove this without using any trigonometry? Every proof I can find uses the ...
1
vote
2answers
3k views

How would one calculate the cosine of an obtuse angle?

How would you calculate the cosine of an obtuse triangle's largest angle? Cos = adj/hyp. But which side is the adjacent side?
5
votes
3answers
772 views

Largest Triangle with Vertices in the Unit Cube

How would one find a triangle, with vertices in or on the unit cube, such that the length of the smallest side is maximized? And what is that length? A lower bound for the length is $\sqrt{2}$, by ...
1
vote
3answers
512 views

Finding angles of triangles

I have what appears to be a $3$-sided triangle: it is two lines on a 180 degree line at the bottom. The bottom left angle is $4x-3$ the top angle is $6x + 3$ and the bottom right angle is not given, ...
3
votes
1answer
337 views

How can I calculate the transformation between two 3D triangles?

I am given the $3$-D coordinates of two triangles. For example: for $\triangle ABC$, the coordinates are: $A=(0, 0, 0)$, $B= (3.37576, 0, 0)$, $C=(5.14131, -2.47202, 0)$ and for $\triangle ...
4
votes
1answer
247 views

Similar - perspective triangles implies corresponding sides are parallel?

In a general homothetic transformation, if two triangles have corresponding sides parallel then the lines joining respective vertices are concurrent at the homothetic center. I was wondering if the ...
4
votes
1answer
1k views

Finding the distance between two gears

I have the following problem: In my class, we did a majorly complicated method to figure this out but I think there is a better way to do this... Here is the exact problem: A belt fits snugly ...
0
votes
1answer
649 views

Get the relation between X and Y axes in triangle based on the degree between

I have a given degree (0 - 360), and based on it, I'd like to be able to calculate the length of X and Y axis of a triangle built on that angle , if the third side of that triangle is equal to 1. I ...
1
vote
1answer
613 views

How can I calculate the transformation of two 3D triangles?

Given two triangle I have the transformation (three rotation followed by three translation)of both the triangles. How can I calculate the transformation between two triangles? A numerical example will ...
0
votes
2answers
2k views

maths - find vertices when 1 vertex and center point is given in polygon

I want to know if there is any general formula to find out vertices (co-ordinates) of a polygon (3 or more equal sides) when following is given: ...
3
votes
1answer
233 views

Help with a geometry problem involving triangles

My geometry book doesn't explain things very well so..... yeah I'm pretty sure that this has a simple answer, but my geometry book words it pretty weird. If triangle RST is congruent to triangle ...
0
votes
3answers
304 views

Calculate the position of Y when position X, distance to Y and the Angle is known

I'm trying to solve this problem: On a regular x/y grid, I have a point A located at position 2,7 (X,Y). I have to place a second point (B) on the grid (somewhere to the right of point A), but I ...
2
votes
2answers
101 views

Calculate x and y coord where line touch

Hi I got a 10 cm long line, and it touches point 1,1 I need to calculate where it touches x and y. If I think of it like an triangle i get the following information. One side is 10 cm. You get ...
6
votes
2answers
4k views

Proof that the angle sum of a triangle is always greater than 180 degrees in elliptic geometry

I've scoured the internet and have found many proofs showing that in Euclidean geometry, the angle sum of a triangle is always 180 degrees. I've also found many proofs showing that in hyperbolic ...
1
vote
1answer
1k views

The formula for finding the steepest curve between a range of x/y coordinates

I know approx what point i want from below diagram by looking at it(red circle), and im pretty sure there is some smart formula that does what im looking for, but how does the formula look like? ...
2
votes
1answer
1k views

Triangle inequality for positive definite symmetric real matrix

Show that \begin{equation} \rho(\mathbf{x},\mathbf{y}) = \sqrt{\sum\limits_{i,j=1}^n a_{ij} (x_i-y_i)(x_j-y_j)}, \end{equation} with $a_{ij} = a_{ji}$, $\mathbf{x} = (x_1,\ldots \;, x_n)$ and ...
2
votes
1answer
1k views

Positioning three circles, all of them touching each other

There are three circles, all of them touching each other. The bottom two circles are laying on an imaginary floor, such that they touch the line g=-r as well. Given are all three radii, r1 (A), r2 ...
0
votes
2answers
191 views

How long is side $c$ in this right triangle if $a = b$?

A right angled triangle has side lengths labeled as so. A common geometric construction that shows three squares sitting upon the sides of a right triangle with lengths A, B, and C However unlike in ...
14
votes
3answers
738 views

The Notorious Triangle Problem

I was told this question by a friend, who said that their friend had thought about it on and off for six months without any luck. I have then had it for a while without any luck either. It is in the ...
10
votes
2answers
2k views

Finding an angle within an 80-80-20 isosceles triangle

The following is a geometry puzzle from a math school book. Even though it has been a long time since I finished school, I remember this puzzle quite well, and I don't have a nice solution to it. So ...
4
votes
3answers
3k views

Find the coordinates in an isosceles triangle

Given: $A = (0,0)$ $B = (0,-10)$ $AB = AC$ Using the angle between $AB$ and $AC$, how are the coordinates at C calculated?
3
votes
1answer
2k views

Are isosceles always and only similar to other isosceles?

In my geometry class last year I remember putting down the statement in a column proof "That all isosceles are always and only similar to other isosceles". I do not remember what I was trying to ...
6
votes
1answer
2k views

RHS Congruency test - What makes 90 degrees different?

RHS is a well known test for determining the congruency of triangles. It is easy enough to prove it works, simply use Pythagorus' theorem to reduce to SSS. I thought that it seems strange that this ...