For questions about properties and applications of triangles

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1answer
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Question related to triangles.

I am stuck at a question: O is a point in the interior of ∆PQR , then which of the following is true: 1)$(OP+OQ+OR)<1/2(PQ+QR+PR)$ 2)$(OP+OQ+OR)=1/2(PQ+QR+PR)$ 3)$(OP+OQ+OR)>1/2(PQ+QR+PR)$ ...
0
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2answers
44 views

Special triangles

I have this question that I have the answer to but no working how to get it, is it by pure memorization of angles or there some steps? Without a calculator, determine, in radians, the angles of a ...
2
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4answers
37 views

Prove that the co-ordinates of the centroid of a triangle is an average of that of vertices

For a given triangle [ABC], how do I prove that the co-ordinates of the Centroid $O_{xy}$ (intersection of the medians) is the average of the individual vertices? $O_x = \left(\frac {A_x + B_x + ...
2
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3answers
51 views

Find out the angles in a given triangle

In a $\Delta ABC$, $a=7$, $c=9$ & $\angle A=36^\circ$. The values of $\angle B$ & $\angle C$ are a.) $94.91^\circ$ & $49.09^\circ$ b.) $95.4^\circ$ & $48.6^\circ$ ...
2
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0answers
21 views

Maximal Triangle on Sphere [closed]

If en equilateral triangle is drawn on the surface of a sphere and expanded till its three vertexes coincide in one point, how many sections result?
0
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1answer
37 views

Summation of Infinite Areas of Triangles Involving Median

A triangle has an area of 2. The lengths of its medians equal the lengths of the sides of a second triangle. The lengths of the medians of the second triangle equal the lengths of the sides of a third ...
2
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1answer
41 views

Maximal Triangle Partitioning in n lines

Recently I was given the following problem at work: Given a 5 pointed star, draw two straight lines through it so that there are 10 minimal triangles within the drawing. It took some work but I ...
0
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4answers
63 views

How to prove using Plane Geometry that Centroid divides in ratio $2$:$1$ [closed]

In $\Delta ABC$ Can any one give me a hint to Prove that the centroid $G$ divides $A$ and Mid point of $BC$ in the ratio $2$:$1$ Using only Plane Geometry.
4
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1answer
118 views

Module of the differential of a function

Given two triangles, $PQR$ and $P'Q'R'$ in $\mathbb{R}^2$, I want to find a bijection $f$ between $PQR$ and $P'Q'R'$ such that: 1) $f$ maps vertices in vertices and sides in sides (i.e. $P$ in $P'$, ...
0
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2answers
53 views

A triangle has sides $2n, n^2+1$ and $n^2-1$ prove that it is right angled

I've tried using Pythagoras theorem but it always results in a silly answer like $n=n^2$ or something. I'm nearly 100% sure this is done with Pythagoras but I'm not sure which way to do it
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1answer
37 views

Parallelogram inside of a triangle dependencies

APMH is a parallelogram inside the triangle ABC. It has a perimeter of 18cm. So my question is could MP divide AB by 2 equal parts AP and PB???
0
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2answers
331 views

Prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third and half as long

The task is to prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long. (Or in vector notation PQ = AB / 2). It should be proved ...
0
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0answers
25 views

Given verticies find the area of the triangle formed

When I looked at this problem I didn't think it seemed all that hard until I actually tried it. The problem is this: Given the rectangular vertices $O(0, 0, 0), P(-1, 2, -3), Q(-2, 3, -4), R(0, 0, ...
0
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1answer
24 views

How to work out the angle of a line passing through a plane

I have a triangular plane composed of three points. From this it it easy to deduce that the plane is in fact composed of two vectors which must touch at some point. because all of this is relative, ...
1
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2answers
68 views

Calculus made easy Exercise 9 Question 4 (Doubt)

A piece of string 30 inches long has its two ends joined together and is stretched by 3 pegs so as to form a triangle. What is the largest triangular area that can be enclosed by the string? I took P ...
3
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2answers
67 views

Expected value of area of triangle

Here is the problem: Let $A$ be the point with coordinates $(1, 0)$ in $\mathbb R ^2$. Another point $B$ is chosen randomly over the unit circle. What is then the expected value of the area of the ...
2
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2answers
46 views

Trigonometry in triangle, can't understand an example from my textbook

I'm stuck with this from a few hours. There is an exercise in my textbook, which is solved and it's must be used as an example, however I can't understand it. Here's the exercises + how it's solved. ...
2
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1answer
20 views

Reference request- Darboux cubic of a triangle

Hi everyone on Math Stackexchange, I'm recently interested in the geometry of a triangle, and my studies now seems to require some knowledge on cubic curves related to a triangle, in particular the ...
0
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0answers
22 views

Inequality based on triangle sides [duplicate]

Let $a,b,c$ be the sides of a triangle. Prove \begin{equation}(a+b-c)(a-b+c)(b+c-a)\le abc\end{equation} I assumed that $a\le b\le c $. Then $(a+b-c)\le a$ and $(a-b+c)\le c$ but $(b+c-a)\ge b$
1
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1answer
63 views

Homework Geometry Triangle Proof Help? (high school)

The question is: Prove that connecting the feet of the altitudes of a given triangle, we obtain another triangle for with the altitudes of the given triangle are angle bisectors. I've tried using ...
0
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0answers
25 views

Find A or B only given the hypotenuse and A to B ratio of a right triangle?

I'm looking for a formula (or set of formulas) that would be able to determine the A, or B value given a right triangle when only C and the A:B ratio is known. I want this mostly for personal use with ...
0
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0answers
80 views

Energy of a Triangle Wave

I want to find the energy of two triangular functions (identical, one above ( S1(t) ) and the other below ( S2(t) ) the x axis, so it should be the same thing). They are shown in the images below. The ...
2
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2answers
380 views

What do you call the point where two lines meet?

This is from a third grader. His example is the point where the hands on the clock meet. It's not pivot. Or "if you start with a dot and make two lines go out from it, on straight up and one to the ...
2
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3answers
76 views

Given point in triangle, prove that it is the centroid

So the question goes like this: Given a triangle ABC, there is a point M within that triangle such that [AMB]=[AMC]=[BMC]. Prove that M is the centroid of the triangle. ([AMC] denotes the area of ...
2
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2answers
24 views

2D geometric relation in a rectangle

I'm trying to implement the Sakoe & Chiba's global constraint for the Dynamic Time Warping algorithm but I'm stuck with a geometrical problem : I'm trying to find the value of d given a, b and c. ...
2
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1answer
39 views

Interior Angle Embedded in a Triangle Embedded in a Circle

With only knowing the angles of $B$, $C$, and $D$ (shown above), is it possible to find the interior angle $A$? And if so, how?
4
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2answers
75 views

Triangle with Ratio of Sides Equal to Ratio of Angles

In an equilateral triangle, the side lengths are in ratio 1:1:1, as are the angle measures. Are there also non-equilateral triangles in which the ratio of the side lengths is the same as the ratio of ...
2
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2answers
48 views

Maximum perimeter for triangle inscribed in circle

How to prove that isosceles triangle has maximum perimeter from all trangles inscribed in circle? I found that from all isosceles trinagles - equilateral has maximum perimeter: Maximum perimeter of ...
2
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2answers
64 views

how many possible acute triangles with perimeter given

How many possible acute triangles exist with perimeter 18? All sides are positive integers. The triangle (7,7,4) is the same as (4,7,7). I need the work in a way that a geometry 9th grade student ...
9
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6answers
867 views

Finding the largest triangle inscribed in the unit circle

Among all triangles inscribed in the unit circle, how can the one with the largest area be found?
3
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2answers
46 views

If $x-2y+4=0$ and $2x+y-5=0$ are the sides of isosceles triangle having area $10$ sq unit .Equation of third side is?

Okay, I know two sides of an isosceles triangle are equal . I have also taken out the intersection points of the lines given in the question . Other than this , I have no clue about how I will find ...
0
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0answers
23 views

Angle for sloped surface intersection

I'm not sure if this is the right SE site for this questions so apologies if it's not. But I've got a question about calculating angles that I can't seem to figure out the maths for. To add a bit of ...
2
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2answers
48 views

An equation involving ratios in a triangle.

In triangle $ABC$, if the incenter is $I$ and $AI$ meets $BC$ at $D$, show that $$\frac{AD}{ID}=\frac{AB+BC+CA}{BC}$$ I tried using similar triangles and got nowhere, couldn't find any use for the ...
1
vote
1answer
64 views

Minimum number of moves required to invert a triangular array of coins?

I cannot find an equation that works WITHOUT rounding. The idea is to find the minimum number of moves to invert a triangle that is made out of counters. The triangle is arranged so that the first row ...
28
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3answers
3k views

I think I see mysterious lines inside triangles—how to prove their existence?

Lately I've been fooling around with points inside a triangle and the sum of their distances from all sides. This was when I noticed a weird behaviour: For each point I chose there always seemed to ...
1
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1answer
37 views

Given the incentre of $\Delta ABC$ and the equations of the angle bisectors what is the locus of the centroid of the triangle $ABC$?

I got this problem on a test yesterday Consider $\Delta ABC$ with incenter $I(1,0)$. Equations of the straight lines $AI$, $BI$, and $CI$ are $x=1$, $y+1=x$ and $x+3y=1$ respectively and $\cot \left( ...
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1answer
30 views

If $\vec{AA_1} + \vec{BB_1} + \vec{CC_1} = 0$ prove that the triangle is equlateral.

The problem states that if $AA_1, BB_1$ and $CC_1$ are the altitudes of the triangle $\bigtriangleup ABC$ and $\vec{AA_1} + \vec{BB_1} + \vec{CC_1} = 0$ then the triangle is equilateral. My solution: ...
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2answers
72 views

Getting different answers using different methods in a geometrical problem

Problem statement: Given a triangle with side lengths 4 and 6, their corresponding opposite angles have a 1:2 ratio. Find the length of the third side. I solved the problem in 2 ways and got as an ...
0
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1answer
110 views

Help determining angle

Let $R$ be the triangle defined by $−x\tan(\theta) \le y \le x\tan(\theta)$ and $x \le 1$ where theta is an acute angle. Sketch the triangle and calculate \begin{equation*} \iint_R(x^2+y^2)\mathrm ...
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2answers
39 views

Help for a problem with inscribed triangles

If we have a triangle $ABC$ with $AB = 3\sqrt 7$, $AC = 3$, $\angle{ACB} = \pi/3$, $CL$ is the bisector of angle $ACB$, $CL$ lies on line $CD$ and $D$ is a point of the circumcircle of triangle $ABC$, ...
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4answers
44 views

Inequality for sides and height of right angle triangle

Someone recently posed the question to me for the above, is c+h or a+b greater, without originally the x and y lengths. I used this method: (mainly pythagorus) $a^2+b^2=c^2=(x+y)^2=x^2+y^2+2xy$ ...
3
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2answers
87 views

How to prove the the addition of tangent is the same as the multiplication? [duplicate]

If A,B,C are angles of a triangle show that: $$\tan A+ \tan B+\tan C = \tan A \tan B \tan C $$ I've tried this many times but I cannot seem to prove it, can someone show me how to solve this ...
2
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3answers
44 views

Triangle relationships

I was wondering if someone can help me actually. You see I came upon this book called Mathematics for Physics by Michael and Malcolm Woolfson. I a presently stuck on the very first exercise and I can ...
0
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2answers
41 views

Calculating the right angled triangle's cathetus

We just started learning the Pythagorean theorem at school and we got a pretty difficult assignment. 5 meter tall bamboo broke and the top of it touched the floor 2 meters from the base of the ...
0
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1answer
35 views

How to prove Thomsen's theorem?

Thomsen's theorem states that given a triangle ABC, choosing a point on AB (but not A or B) and doing the internal path parallel to AC till reaching BC, and then doing the path parallel to AB till ...
2
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3answers
59 views

Determine length from sketch

I have a simple problem that I need to solve. Given a height (in blue), and an angle (eg: 60-degrees), I need to determine the length of the line in red, based on where the green line ends. The ...
1
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1answer
58 views

What is the name of this (circumscribed) triangle?

I am meeting the following triangle more and more in my investigations of ideal triangles in the Beltrami Klein model of hyperbolic geometry. That made me wonder: is there a name for it? (And does it ...
3
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1answer
50 views

Triangle Center Midpoint

Consider the following construction of a triangle center: (The method could also be easily generalized to any shape with finite perimeter) For each point $X$ on the triangle, find point $X'$ such ...
2
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2answers
50 views

Is there a measure for how thin or squat a triangle is?

Is there a measure for how thin or squat a triangle is? Similar to eccentricity for ellipses.
3
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1answer
71 views

Is there an equidissection of a unit square involving irrational coordinates?

An equidissection of a square is a dissection into non-overlapping triangles of equal area. Monsky's theorem from 1970 states that if a square is equidissected into $n$ triangles, then $n$ is even. ...