For questions about triangles

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1answer
317 views

Sum of Angles in a Triangle.

Can anyone please explain how to form a better idea in understanding Sum of measures of angles in a triangle are 180 degrees.
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1answer
93 views

Finding a point which is constrained to 3 other points.

Is there an easy way to find the 4th point given 3 fixed points and a different minimum length between the 4th point and each of the 3 points? Similar to this question, but with non-fixed minimum ...
3
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1answer
373 views

Maximum triangle area

I have a small problem. Consider I have a triangle. Which maximum area can it cover if two of his medians are 3 and 8? I think I'll need to use derivative here, but firstly I need to find a function ...
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2answers
328 views

How do i find this angle in a right triangle?

So i'm writing a program, and i need to write a method that will give me the angle of a specific angle of a triangle when i know only the adjacent length and opposite length. I know that "tan(A) = ...
3
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1answer
178 views

Algebra question about Triangle Interiors

I was reading about Triangle Interiors on Wolfram Alpha: http://mathworld.wolfram.com/TriangleInterior.html and they have a simple equation: $$\mathbf{v} = \mathbf{v}_0 + a\mathbf{v}_1 + ...
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1answer
260 views

How do we derive the direction formula for longitude latitutude

θ = atan2( sin(Δlong).cos(lat2), cos(lat1).sin(lat2) − sin(lat1).cos(lat2).cos(Δlong) ) Does it take into account that we may be dealing with a trapezoid rather than a rectangle ...
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2answers
526 views

The incenter and Euler line.

It seems well known that the incenter of a triangle lies on the the Euler line if and only if the triangle is isosceles (or equilateral, but that is trivial). Searching the internet, I could not find ...
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0answers
200 views

Uniform Random Points on a triangle using only edge plane normals

For a triangle $ABC$ in 3D (each point has x, y, z coordinates) is it possible to generate uniform random points on the triangle from only the following data: Normal of the triangle plane $N = ...
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4answers
462 views

Proving $a^2+b^2=c^2$ where $a,b,c$ are side lengths of a right triangle.

Proving $a^2+b^2=c^2$ where $a,b,c$ are side lengths of a right triangle. First, I have never done a proof before, sorry I am so poor here. I have spent many hours but my actions have mostly used ...
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1answer
265 views

How to describe foсi of en ellipse inscribed in the triangle thru triangles angles points?

I was looking at Marden's theorem and could not help but wonder how foсi of en ellipse inscribed in the triangle can be described thru triangles angles points?
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2answers
253 views

Geometric inequality: $2r^2+8Rr \leq \frac{a^2+b^2+c^2}{2}$

Suppose $a$, $b$, and $c$ are the lengths of the sides of a triangle, and $R$ and $r$ are its circumradius and inradius respectively. How can one prove the following inequality? $$2r^2+8Rr \leq ...
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2answers
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Is an equilateral triangle the same as an equiangular triangle, in any geometry?

I have heard of both equilateral triangles and equiangular triangles. (For example, this sporcle quiz lists both.) Are these always equivalent, regardless of geometry? I know they are the same in ...
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4answers
530 views

Simple trigonometry question (angles)

I am starting again with trigonometry just for fun and remember the old days. I was not bad at maths, but however I remember nothing about trigonometry... And I'm missing something in this simple ...
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3answers
719 views

general triangle angles and lengths

Pythagoras shows us how to find the 3rd side length on a right angled triangle where the two lengths connected by the 90 degrees are known. Additionally there is a surprisingly short equation that I ...
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2answers
683 views

Sangaku: Show line segment is perpendicular to diameter of container circle

"From a 1803 Sangaku found in Gumma Prefecture. The base of an isosceles triangle sits on a diameter of the large circle. This diameter also bisects the circle on the left, which is inscribed so that ...
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3answers
302 views

Systems of equations finding right triangles

I need help setting up the equation for the question, "Find all right triangles for which the perimeter is $24$ units and the area is $24$ square units." I know that the area is $A = \frac12 b h$ ...
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1answer
77 views

Quadratic Equation related question.

So here's the question : The hypotenuse of a right triangle is $3 \sqrt 5$ cm. If the smaller side is tripled & the larger side is doubled, the new hypotenuse will be $15$ cm. Find the length of ...
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3answers
215 views

Intuition around why Sine of X angle always equals same result.

My understanding so far. Sine represents a ratio of two sides of an interior angle within a right angle triangle. So given the three lengths of a triangle you can find the sine of any of the 3 ...
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4answers
409 views

Right triangle where the perimeter = area*k

I was doodling on some piece of paper a problem that sprung into my mind. After a few minutes of resultless tries, I advanced to try to solve the problem using computer based means. The problem ...
2
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2answers
322 views

Isosceles Trapezium problem

I came across a problem in a certain quiz which I couldn't solve. Here it is reproduced: Since $BX$ is midpoint of $AB$, $AB = CD = 2$ . Now $AD$ and $BC$ remain to be calculated. How can the right ...
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2answers
175 views

What is wrong with my algorithm (finding if the origin is within a triangle's interior)?

I am working on Project Euler Problem 102 and I thought I had a solution, but it seems I do not. Now, don't give me the solution. I know I'm on the right track. What I want to know is why my method ...
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1answer
557 views

Computing circumcenter of triangle in 2D with MATLAB

I'm writing a finite volume program over a 2D triangular mesh, and at one point I need to calculate the circumcenters of the triangles. The equation given in class and that on Wikipedia give different ...
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6answers
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How many triangles are there?

The question is how many triangles are there in the following picture? I have thought to solve it by creating a formula based on the angles of the lines starting from the bottom of each side. I ...
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2answers
7k views

Can we find the perimeter of a triangle given only its base and height?

How do you find the perimeter of a triangle that you only have the base and height measurements for? Please use ENGLISH and not difficult mathematical formulas! I understand little algebra so avoid ...
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2answers
113 views

Showing whether two numbers are equal or not

$\dfrac{\sin (2x+y)}{\sin (2x)} =\dfrac{\sin (x+2y)}{\sin (2y)}$,where $0<x,y\le\dfrac{\pi}{4}$ . Can I show that $x=y $ or find two numbers $x,y$ such that $x\not=y$?
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2answers
418 views

How to show angle bisector in triangle ABC?

I was giving the following question: Let ABC be a triangle. The outer angle bisector of B and the outer angle bisector of C meet in point O. I need to show that AO is the angle bisector of A. In ...
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1answer
1k views

How to prove we could use mass point geometry to solve all the triangle problem involving ratio between line segment and transversal in a triangle?

what is an easy way to prove that use mass point geometry to solve a problem in the link i provide that is involving cevians in a triangle is same as using the other way in euclidean geometry or ...
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2answers
358 views

How do I prove that the orthocenter of a triangle is barycentre of its vertices?

Let's say I have a triangle $ABC$, the middle of the sides are called $A'$, $B'$ and $C'$. I have proved that $\Omega$, the orthocenter of $ABC$, is the barycentre of $A'B'C'$ ...
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1answer
338 views

Find 2nd leg of right triangle with known leg and perimeter

This is probably a very basic question for this site, but it got me stumped. For a right triangle with one leg (A) and perimeter (L) given, how do I calculate the hypotenuse (C) and second leg (B)? I ...
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1answer
340 views

Triangle question

I am not able to solve this question from chapter "Similar & Congruent Triangles" in my book. Can some one help to calculate AC? .
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4answers
1k views

probablity of random pick up three points inside a regular triangle which form a triangle and contain the center

what is the probablity of random pick up three points inside a regular triangle which form a triangle and contain the center of the regualr triangle the three points are randomly picked within the ...
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3answers
163 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 ...
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1answer
362 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 $AC$.
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2answers
124 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 ...
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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)
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4answers
179 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
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1answer
159 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? ...
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2answers
119 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, ...
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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 ...
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2answers
129 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 ...
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2answers
407 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 ...
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1answer
83 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 ...
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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 ...
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2answers
182 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 $(x_0,y_0)$, ...
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3answers
511 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 ...
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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 ...
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2answers
773 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?
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2answers
175 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
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4answers
736 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 ...
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0answers
220 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 ...