For questions about triangles

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4
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2answers
129 views

In triangle, $\sin\frac{A}{2}+\sin \frac{B}{2}+\sin\frac{C}{2} -1 = 4\sin \frac{\pi -A}{4}\sin\frac{\pi -B}{4} \sin\frac{\pi-C}{4}$

To prove $$\sin\frac{A}{2}+\sin \frac{B}{2}+\sin\frac{C}{2} -1 = 4\sin \frac{\pi -A}{4}\sin\frac{\pi -B}{4} \sin\frac{\pi-C}{4}$$ My approach : $$ \begin{align} \text{L.H.S.} & = ...
0
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0answers
20 views

How to prove that P,G, and K are collinear from this triangle problem?

Given: triangle ABC. We choose point Q at AC, P1 and P at BC, and R at AB, such that: AR/RB= BP/PC= CQ/QA= CP1/P1B Suppose G is centroid of triangle ABC, and K= AP1 ∩ RQ. How to prove that P,G, and ...
2
votes
1answer
84 views

What is the converse of the triangle inequality?

It's usual when presenting a theorem to also present its converse. Surprisingly, I've never seen the triangle inequality's converse stated. Triangle inequality: If the sides of a triangle are a, b, ...
1
vote
1answer
34 views

How to prove that:$ BC^2= 3CM^2 + AC^2 $from this triangle problem?

In the triangle $\triangle ABC$, angle $\angle A$ is larger than angle $\angle B$. We choose points $M$ and $N$ at $AB$ such that $AM=MN=NB$. How to prove that: $BC^2= 3CM^2 + AC^2$? Which ...
0
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1answer
19 views

what is the measure of angle ECD from this following triangle problem?

In triangle ABC, AB is larger than BC. Then, we choose point E outside the triangle such that BE=BC. We extend line AB to D, such that BD=BC. BF is angle bisector of angle ABC. If DC is parallel ...
4
votes
2answers
61 views

How to prove that the angle between two sides of that triangle is less than 60 degree?

The product of two sides of triangle is equal to 8*(R*r) where R is circumradius of this triangle, and r is inradius of this triangle. How to prove that the angle between two sides of that triangle ...
0
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2answers
56 views

MCA entrance question

In triangle $ABC$, the value of $\ \displaystyle \sum_{r=0}^n\ ^nC_ra^rb^{n-r}\cos(rB-(n-r)A)$ is equal to (a) $c^n$ (b) $b^n$ (c) $a^n$ (d) $0$ I have no idea how to start ...
0
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0answers
31 views

I stumbled when i saw this (Travelling Salesman related)

I have here 5 locations like below I then have a tour of 1,2,3,4 (point 5 isn't inserted into tour yet) like below I then find the shortest addition distance to include point 5 into tour, the ...
5
votes
2answers
153 views

Minimum area of a triangle

In triangle inscribed circle with radius $r = 1$ and one of it sides $a=3$. Find the minimum area of triangle? Ans = 5.4 My reasonings: $BC = a$, $AC = b$, $AB = c$ $AD=AF=x$ $FC=CE=y$ ...
0
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0answers
14 views

How to prove that angle EDL is same with angle ELD in the following triangle problem?

Given: triangle ABC with angle A equal with 60 degree. We choose points D and M at AC, points E and N at AB, such that DN perpendicular to AC and EM perpendicular to AB. If L is midpoint of MN, ...
1
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2answers
86 views

Three circles with two common points

Let $ABC$ be a triangle of any type and $A_1,B_1,C_1$ the feet of the heights. Denote $M,N,P$ the orthogonal projections of the point $A$ onto the lines $B_1C_1,C_1A_1$ and $A_1B_1$. The circes ...
0
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3answers
49 views

Triangle inequality and its equality

How do I prove this? $$|x+y|=|x|+|y|\Leftrightarrow xy\geq0$$ I tried to use the triangle inequality, but I didn't get so far... Thanks!
0
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2answers
55 views

Why can I not use an equation using proportions to solve this triangle problem?

It is difficult to see the picture of the problem. The question is "What are the lengths of AC and AB?" What is given is a right triangle, ABC. Angle B is 30 degrees and BC is 7.0 distance. The ...
0
votes
1answer
71 views

Competition math geometry question

The perimeter of triangle ABC is $36$, and its area is $36$. Compute $\tan\frac{A}2 \tan\frac{B}2 \tan\frac{C}2$. I found that the answer is $1/9$, but I was not able to find a reason for this. Could ...
0
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1answer
46 views

How to prove that $DE=EF +DG$ from this following triangle problem?

Given a right triangle $ABC$, where $C$ is a right angle. We choose points $G$ at $AC$ and $F$ at $BC$, and $D$ and $E$ at $AB$. We draw right triangles $AGD$ and $EBF$, such that $\angle AGD= ...
2
votes
1answer
47 views

Solution for the value of an angle of a triangle ABC

Find value of angle m< DBC Where $$BD=DC=AC$$ $$2(m\langle BAC)=14(m\langle ABD)=7(m\langle BCD)$$ I tried hard but im out of ideas now, I know the answer is 20 but I want to know how, thanks ...
2
votes
1answer
22 views

tetrahedron height

I've got the next figure: Now I would like to calculate the height, so from D to the plane ABC. First, I've tried with a coordinate system, but it's to difficult to take these distances into ...
1
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0answers
36 views

solve this complex triangle question ?

,D,E,F are midpoint of triangle ABC on sides BC , CA , AB. The feet of the altitudes from A,B,and C are P,Q and R. h is the orthocentre and O is the circumcentre . Then prove 2OD=AH. The nine ...
0
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3answers
93 views

Finding area of sector inside an triangle

I have been asked this question from a junior and could not solve the question in a simple way. I am asking help on this platform. For a triangle $ABC$, Points $D, E$ on $AB$, where ...
0
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1answer
20 views

Calculate regular or equilateral triangle altitude with radius only possible?

I need to calculate the altitude of a regular triangle (equilateral) but i only have the radius (polygon radius) available (http://www.mathopenref.com/polygonradius.html). I have been searching for ...
0
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2answers
48 views

To find base and height of an isosceles trangle if sides and area are give

The area of an isosceles triangle is $60cm^2$ and the length of equal side is $13cm$. Find height and base.
4
votes
1answer
118 views

Length of median extended to the circumcircle

A triangle has side length $13,14,15$, and its circumcircle is constructed. The median is then drawn with its base having a length of $14$, and is extended to the circle. Find its length.
2
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0answers
87 views

Hijacked Malaysian plane position geometry

Sorry to get geeky in the midst of a tragedy and likely horrible crime, but does anyone know how they got this diagram showing the possible last known positions of the possibly hijacked Malaysian ...
0
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1answer
137 views

Maximum perimeter of an isosceles triangle inscribed in the unit circle?

So I have seen this question asked before but with variations (circle of radius 4, and an equilateral triangle) and so I am hoping for an answer on how to do this. After looking around I saw that ...
1
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1answer
29 views

Solving integral including a triangle

How can I solve this integral? Image link: http://oi61.tinypic.com/2jeoga1.jpg I tried to solve it: x^2/2 from 4 to 0. [(4^2/2)-(0^2/2)]=8 but its wrong. Do I have to multiply base*height/2 because ...
-1
votes
5answers
120 views

Trigonometry Question (finding the sin, cos, cosec etc on a right-angled triangle)

For the right-angled triangle $\widehat{PQR}$, where $\overline{PQ} = 9\text{ cm}$, $\overline{QR} = 40\text{ cm}$ and $\overline{PR} = 41\text{ cm}$, give the value of: a) $\sin \hat{P}$ b) $\cos ...
3
votes
2answers
84 views

Find the maximum angle possible

$P$ is a point on the $Y-axis$ . Find the maximum possible value of $\angle APB$ where $A=(1,0)$ and $B=(3,0)$. Here is how I solved the problem. Suppose $P=(0,k)$ . Then using the cosine formula we ...
0
votes
1answer
24 views

Calculate an angle between time 00:00 and a mouse cursor position

I have to build a timepicker where user clicks on a clock like circle and it gives a time. Once I have cursor position I think that all I have to do is to calculate an angle between time 00:00 and a ...
1
vote
1answer
40 views

Similar Triangles with proportions

In $\triangle ABC$, $AB=8, BC=7, CA=6$, and side $BC$ is extended to point $P$, so that $\triangle PAB$ is similar to $\triangle PCA$. Find the length of $PC$.
0
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2answers
42 views

Prove that this is an isoceles triangle

I'm trying to solve a problem here. It says: "Prove that a triangle is isoceles if $\large b=2a\sin\left(\frac{\beta}{2}\right)$." $B-\beta$ I've tried to prove it but I can't Can anyone help me?
0
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1answer
25 views

Representation of a Triangle

In this document, a Triangle is represented as: $$ T(s,t) = B + sE_0 + tE_1\\for~all~(s,t)\in D=\{(s,t):s\in[0,1], t\in[0,1],s+t\le1\} $$ Can someone explain this representation of a Triangle?
0
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1answer
40 views

Regular pentagons inscribed in a triangle

I know that inscribing a square into a triangle has been researched a lot. But has there been any research on the problem inscribing a regular pentagon into a triangle? Can anyone tell me more on the ...
2
votes
2answers
28 views

Trying to triangulate from two (or three) known points.

If I'm at an unknown location, but I have visible points (monuments) that I know the location of, and I can measure the angle between them, I should be able to determine my location. I'm thinking ...
4
votes
1answer
214 views

Inequality in triangle involving side lenghs, medians and area

A, B and C are the vertices of a triangle. Denote $m_a$, $m_b$ and $m_c$ the medians from A, B and C. Prove the inequality: $$\sum_{cyc}{a^2bcm_a}\geq\sum_{cyc}{cS(a^2+b^2)}$$where a, b and c are the ...
0
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2answers
45 views

Scale sides of a triangle

If I have a triangle with sides A B and C, how can I scale the triangle down to one that has sides A + B = 1? E.g, if I have the triangle ABC where length of A = 45, length of B = 55 and length of C ...
0
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0answers
35 views

Triangle rotating freely around origo, need to calculate corners.

Lets say I have a triangle with corners $(-1, -2)$, $(0, 2)$ and $(1, -2)$. I specify a line that is exactly one side of the triangle, for example $(-1, -2)$, $(0, 2)$. Now, I rotate the triangle ...
0
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3answers
31 views

Finding the sides of Right Triangle when only angles are given

I have a question in which a Right angle triangle is given, one of the angle is 50 degree. Since it is a right angle therefor other two angles are 90degrees and 40degrees. The perpendicular of this ...
0
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1answer
40 views

How to extract all the points from a noisy surface?

I have points representing a bridge like in this picture: My goal is to get all the points that are in the red box. These points all share a common surface that is not necessarily planar. The ...
0
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1answer
87 views

Fourier Transform for triangular wave

Could someone tell me if I've worked this out right? I'm unsure of the process, especially the final parts where I convert it to a sinc function. Please let me know if I've made mistakes anywhere ...
8
votes
1answer
72 views

Trigonometric Substitution

I am having trouble with this problem even though everything I did seemed right to me since we went over a similar one in my class. I used the method of setting up a triangle, my hypotenuse is ...
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2answers
72 views

Proving the diagonals of a quadrilateral are equal

This is an easy question but it is troubling me a lot: $ABDC$ is a convex quadrilateral, with $AB=BC=AC$ and $\angle BDC=150^{\circ}$. Show that its diagonals are equal. I have tried fiddling with the ...
2
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2answers
81 views

Sine defined for a triangle inscribed in a circle with a diameter of one

Let a circle be drawn with a diameter of one (and thus a radius of one half). Then let a triangle with vertices A, B, and C be inscribed in the circle (i.e. points A, B, and C are arbitrary points on ...
3
votes
3answers
112 views

Prove Parallelogram Area Is Twice Triangle Area

I thought this would be easy but I can't seem to find the answer. Edit: I did my best to draw the diagram: $\overline{EC}=\frac{1}{3} \overline{AC}, \overline{AF}=\frac{1}{3} \overline{AB}, ...
1
vote
2answers
37 views

issues with geometry triangle

$4$ line drawn parallel to base of triangle such that they are equidistant.if the area of the most bottom part is 4 sq cm. find area of triangle? MY THOUGHTS : being weak in geometry i couldn't make ...
0
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6answers
114 views

New area of triangle if sides are halved

My question is that if we have a triangle, and we divide each of the side by 2 to get a new triangle, what will be the area of the new triangle in context to the original triangle? Please provide a ...
1
vote
1answer
108 views

How do I solve for the height of a triangle?

The basic triangle looks something like this: How do I solve for $h$? As an example, in one problem I was given $b = 45, c = 42, \angle C = 38^\circ$ I understand how $h$ divides $\triangle ABC$ ...
3
votes
2answers
60 views

Question about pythagorean triples

Given a,b,d natural numbers. Suppose (a, b) are two legs of a pythagorean triple. Also suppose (a, b+d) are two legs of another pythagorean triple. I'm looking for a way to show that given the ...
0
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2answers
82 views

Solving all possible triangles?

So we're doing oblique triangles -- Law of Sines and all that good stuff =). I have a bunch of problems that ask you to solve for "all possible triangles that satisfy the given conditions". For ...
3
votes
1answer
40 views

Odd and Even Triangles

I am about to make a report on the topic of characterization of line graphs then I came across the terms "odd triangles" and "even triangles". Does anyone know what these terms mean? To elaborate, I ...
3
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0answers
50 views

Howto prove that $\sum_{cyc}\cos\frac{A}{2}\cos\frac{B}{2}\le\frac{1+2\sqrt{2}}{2}+\frac{7-4\sqrt{2}}{R}r$

let $ABC$ is a triangle with inradius $r$ and circumradius $R$. Show that ...