For questions about properties and applications of triangles

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2answers
30 views

Find perimeter and angle of triangle using three 3d vectors .

Given the following, three vectors: $$\vec{a} = 3\mathrm{i} - 2\mathrm{j} + 5\mathrm{k}\\\vec{b} = \mathrm{i} - 6\mathrm{j} + 6\mathrm{k}\\\vec{c} = 2\mathrm{i} + 3\mathrm{j} - \mathrm{k},\\$$ find ...
0
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2answers
396 views

How to find the inradius of a triangle with given side lengths?

I need to find the inradius of a triangle with side lengths of $20$, $26$, and $24$. I know the semiperimeter is $35$, but how do I find the area without knowing the height? Thank you.
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1answer
302 views

A problem on triangle and its perpendicular bisectors.

I'm trying to solve the following problem : "In △ABC, coordinates of $B$ are $(−3, 3)$. Equation of the perpendicular bisector of side $AB$ is $2x + y − 7 = 0$. Equation of the perpendicular ...
3
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2answers
60 views

How to find the number of right angled triangles with integer sides and inradius 2009 ..

Problem : How to find the number of right angled triangles with integer sides and inradius 2009 Please help on this as I am not getting any clue how to proceed this problem. I know that ...
3
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1answer
348 views

Geometry - optimal 2D mesh between X expendable points

Say you have X points on a plane. If you connect two points, you form a line. Connecting three points forms a triangle. A line cannot cross a line, and a smaller triangle cannot be created inside a ...
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2answers
60 views
0
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1answer
500 views

Calculate 3rd point of a triangle, given 2 points and all angles in 2D

I have stumbled upon an interesting problem. I tried to find an answer here but there are just too many similar threads which did not really help me, so I was trying to figure it out by myself. The ...
0
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1answer
972 views

Find coordinates of vertex in right triangle

I have a right triangle with known points $A(x_1,y_1), B(x_2,y_2)$ and known cathetus $AC$ and $BA$. I need to find the coordinates of point $C$.
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1answer
328 views

Can an equilateral triangle be an isosceles triangle, too?

I've looked in a math book that an isosceles triangle has at least two congruent sides. I also know that the words "at least" mean this symbol: $\ge$, which means "is greater than or equal to" or "is ...
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0answers
23 views

Golden Ration Generalization [closed]

Please help me to solve this exercise. (Sorry for my English) Given a natural number $p$ split a segment into two lengths of $a$ and $b$ with a> b such that: $\frac{a+b}{a}=p\frac{b}{a-b}$ ...
4
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7answers
186 views

Proving $ \frac{1}{c} = \frac{1}{a} + \frac{1}{b}$ in a geometric context

Prove or disprove $$ \frac{1}{c} = \frac{1}{a} + \frac{1}{b}. $$ I have no idea where to start, but it must be a simple proof. Trivia. This fact was used for determination of resistance of two ...
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1answer
53 views

Proving that $ ABC$ is similar to $DQP$

Let $G$ be the centroid of triangle $ABC$. Let $D$ be the midpoint of $BC$. A line through $G$ parallel to $BC$ meet $AB$ at $M$ and $AC$ at $N$. $MC$ meets $BG$ at $P$ and $NB$ meets $CG$ at $Q$. ...
0
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2answers
35 views

How would you find the length of a side of a triangle where 2 sides are known and the length of a line in the middle is also known?

How would you find the length of a side of a triangle where the other 2 side lengths are known and the length of a another line that meets at the same point is known? I know there has to be an answer ...
1
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1answer
49 views

How to prove AKN is an equilateral triangle? [closed]

Let $ABC$ be an equilateral triangle. $P$ is the midpoint of arc $AC$ of its circumcircle, and $M$ is another point on the same arc. $N$ is the midpoint of $BM$. $K$ is the foot of the perpendicular ...
2
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0answers
40 views

Alternative proof for the equality of two angles in an isosceles triangle.

From the answers of my previous question, I got an idea to prove equality of two angles in an isosceles triangle. In that question the equality of two angles in a right-angled-isosceles triangle was ...
2
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0answers
28 views

Generalization to higher dimensions of a statement about plane triangles

Let $\Delta=\Delta ABC$ be a plane triangle with area $F_\Delta$ and let $P$ be a point in $\Delta$. Draw lines through $P$ parallel to the sides of $\Delta$; then $\Delta$ is decomposed into three ...
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2answers
7k 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
1k views

Ratio of angle divided 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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3answers
9k 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)?
3
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3answers
883 views

Right-angled isosceles triangles

If a right-angled triangle is isosceles then the other two angles must be equal to $45^\circ$ ? Is this always the case or are there other possible right-angled isosceles triangles?
3
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3answers
80 views

How is $\sin 45^\circ=\frac{1}{\sqrt 2}$?

I've been reading about the proof of $\sin 45^\circ=\dfrac{1}{\sqrt 2}$ in my book. They did it as following, let $\triangle ABC$ be an isosceles triangle as shown, Since the triangle is isosceles ...
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2answers
40 views

Elementary problem in geometry [closed]

The problem asks to find the angle at $C$. The distance between $A$ and $B$ is $12 \space m$ and the distance between $B$ and $C$ is $8\space m$. Anyone got an idea?
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1answer
22 views

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)$(OP+OQ+OR)>1/2(PQ+QR+PR)$ ...
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2answers
41 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 ...
3
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1answer
92 views

Prove that the intersection of $BM$ and $CN$ is on the circumcircle of triangle $ABC.$

Let $P$ and $Q$ be on segment $BC$ of an acute triangle $ABC$ such that $\angle PAB$ = $\angle BCA$ and $\angle CAQ = \angle ABC$.Let $M$ and $N$ be the points on $AP$ and $AQ$, respectively, such ...
4
votes
1answer
115 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 $P'$, ...
2
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4answers
32 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
47 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.) $95.4^\circ$ & $48.6^\circ$ ...
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0answers
38 views

Why do the triangles in the unit circle after 90 degrees look like this?

e.g. any triangle in the unit circle has one side (the hypotenuse) which is always positive? why is it positive? I edited this picture http://mathforum.org/mathimages/imgUpload/Trig_refangle.jpg to ...
2
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0answers
18 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?
2
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1answer
31 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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1answer
33 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 ...
0
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4answers
57 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.
11
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1answer
175 views

Number of ways to dissect a square into triangles of equal area

Monsky's theorem states that it is impossible to dissect a square into an odd number of triangles of equal area. If $n$ is an even integer, I am interested in the number of ways of dissecting a ...
0
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2answers
38 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
35 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???
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7answers
970 views

An alternative proof of 30-60-90 theorem/

A 30-60-90 theorem in Geometry is well known. The theorem states that, in a 30-60-90 right triangle, the side opposite to 30 degree angle is half of the hypotenuse I have a proof that uses ...
28
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0answers
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 ...
0
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2answers
50 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 ...
4
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1answer
439 views

How to calculate Fermat point in a triangle most efficiently?

I am aware of this question, but mine is a bit more specific. I want to find the coordinates of the Fermat point for a given triangle. Assuming that no angle in the triangle is larger than 120 ...
0
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0answers
23 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, ...
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0answers
28 views

The minimum perimeter and maximum height of a triangle under constraints [unanswered] [duplicate]

I need a second oppinion: Please, i need urgent help for my very difficult question, many days ago i ask this question, now , i only have 7 days for present my http://triancal.esy.esTriancal (online ...
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2answers
60 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 ...
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1answer
22 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, ...
3
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2answers
49 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 ...
1
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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
votes
1answer
18 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
21 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 $(b+c-a)\ge b$
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1answer
60 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 ...
3
votes
2answers
5k views

when to use sine vs cosine vs tangent

I'm a little confused about how you choose to use either sine or cosine or tangent over the others. Are they interchangeable given the same information you have about a right triangle? What are the ...