For questions about properties and applications of triangles

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2
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1answer
34 views

Spherical Triangle

I know that the area for a spherical triangle is calculated as Area $= r^2(a+b+c-\pi)=r^2E$ where $E= (a+b+c-\pi)$ is the spherical excess I was wondering why do you have to multiply by $r^2$ (the ...
0
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1answer
46 views

jensen inequality in trigonometry [duplicate]

Can anyone help me how to prove $\sin A + \sin B + \sin C \leq \frac{3}{2} \cdot \sqrt[2]{3} $ I have idea use jensen but how to use it here?
3
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2answers
51 views

Finding angles plane geometry

$\Delta ABC$ is obtuse on $B$ with $\angle ABC = 90 + \frac{\angle BAC}2$ and we have a point $D \in AC$ (in the segment, I mean D is in between A and C) such that $\angle BDA = \angle ABD + ...
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4answers
66 views

Limit of ratio of areas of triangles defined by tangents to a circle

Let $AB $ be an arc of a circle. Tangents are drawn at $A $ and $B $ to meet at $C $. Let $M $ be the midpoint of arc $AB $. Tangent drawn at $M $ meet $AC $ and $BC $ at $D $, $E $ respectively. ...
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1answer
27 views

Point in a triangle plane determining any angles

Let $\triangle{ABC}$ be an arbitrary triangle. Is it true that for any angles $\alpha, \beta,\gamma\in [0,2\pi]$ with $\alpha+\beta+\gamma=2\pi$ one can find a point $M$ in the plane of the triangle ...
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0answers
24 views

Finding a specific weight triangle in a graph

It is possible to find the minimum weight of the triangles in a graph by using the following: Let G = (V, E; w) with w : V ∪ E → {−W, . . . , 0, . . . , W} ∪ {∞}, and V = {1, . . . , n}. Set D = ...
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2answers
38 views

Ratio of parts of a triangle

In the diagram above, segment DE is parallel to segment BC and the ratio of the area of triangle AED to the area of trapezoid EDBC is 1:2. How can I find the ratio of AE to AC? So far, I got the ...
3
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2answers
110 views

Proof of a geometric statement

If $D$ is a point inside a triangle $\triangle ABC$ then how the following statement is true. statement: $AB+AC>BD+DC$. I have tried in the following way but it seems to me defective. ...
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2answers
68 views

Trigonometry - how to find angles of triangle within another triangle?

What are the angles of angle 1 and 2? I don't see how any of them could be corresponding angles... The adjacent side of angle 2 is parallel to the hypotenuse of the bigger triangle, just to make ...
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0answers
74 views

Angle of Sine wave

How you do calculate angle of sine wave? Here in this example you can see the angle as the sine wave goes either side of the graph http://www.mathopenref.com/triggraphsine.html. For producing the sine ...
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1answer
567 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 ...
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2answers
26 views

Name for line segment parallel to triangle base

In describing an elegant construction of a regular pentagon, i'm struggling to find a nice way of describing the following: A line segment starting at a point partway up one side of a (in this case, ...
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2answers
47 views

Determine if a triangle is right angled with only coordinates

What is the easiest way to determine that, given 3 coords, they DON'T form a right angled triangle? EG, (0, 0, 0), (0, 1, 0), (1, 0, 0) - forms a right angled triangle (0, 0, 0), (0, 1, 0), (1, 0.5, ...
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1answer
22 views

How to find a function that maps an element to row number in a triangle of integers?

This is a triangle of integers 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ........ Is there some function that could map ...
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0answers
29 views

Quantifying the similarity of two line segments with a third line segment

In the program I'm developing, there are a large number of lines, and one point. One of the lines will split into two lines, the first line beginning with the original's first point and ending with ...
2
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2answers
35 views

The area of a triangle is $54\sqrt{6}$ square units. Find the lengths of the sides: $5x,6x,7x$

I realize I can use Heron's formula for this question. I did $54\sqrt{6}=\sqrt{9x\cdot 3x\cdot 4x\cdot 2x}$ but from there I must have done something wrong. Thanks for the help.
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0answers
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Calculate the area of a triangular field, knowing that two and 1 angle.

Hello so this problem came up while I was studying trig. and I seem a bit stuck: Calculate the area of a triangular field, knowing that two of its sides measure $80$ m and $130$ m and between them is ...
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1answer
40 views

Problem involving rhombus and its diagonals and height

If I know that one of the heights of a rhombus splits its longer diagonal in 2 segments equal to 7 and 11, how can I find the length of the base of the rhombus?
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4answers
372 views

Concentric Equilateral Triangles

I'm currently researching a particular dynamical system that is very geometric in nature. As part of this, I need to prove the following results (the second obviously implies the first). They are ...
2
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2answers
59 views

Simplest proof that the edge of an inscribed equilateral triangle bisects the radius

Context: I am giving a short talk on the Bertrand Paradox to a mixed group, many of whom have studied mathematics at a higher level some years ago. The point of the talk is the philosophical ...
0
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1answer
33 views

How to prove that perpendicular bisector of line joining altitudes also bisects the side?

Let ${D,E,F}$ be the feet of the altitude from ${A,B,C}$ in a ${\triangle{ABC}}$. Prove that the perpendicular bisector of ${EF}$ also bisects ${BC}$.
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1answer
32 views

Forbidden zones for circumcenter

Given a triangle $ABC$, let $A'$ be the middle point of $BC$, $B'$ the middle point of $AC$ and $C'$ the middle point of $AB$. It is well-known that the circumcenter of $ABC$ is the orthocenter of ...
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2answers
69 views

Let $a$, $b$ and $c$ be the three sides of a triangle. Show that $\frac{a}{b+c-a}+\frac{b}{c+a-b} + \frac{c}{a+b-c}\geqslant3$

Let $a$, $b$ and $c$ be the three sides of a triangle. Show that $\frac{a}{b+c-a}+\frac{b}{c+a-b} + \frac{c}{a+b-c}\geqslant3$
0
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1answer
38 views

In a right triangle ABC with AH as height prove that BC, BA, BH form geometric progression.

Let's have a right triangle ABC(A=90 grades) and AH as height. Prove that BC, BA, BH form a geometric progression. Well is saw that they were similar triangles and showed that $$BC/AC=AC/HC=AB/AH$$ ...
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2answers
74 views

Is there an equation that represents the nth row in Pascal's triangle?

I'm doing binomial expansion and I'm rather confused at how people can find a certain coefficient of certain rows. For example, if a problem was $(2x - 10y)^{54}$, and I were to figure out the ...
2
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2answers
75 views

How to find the position of point S on a tetrahedron if all segments are known?

I have been having this problem at work in this software I am writing. This question looks like a homework question but it is not... I promise. I took my problem and generalized it to a more simple ...
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2answers
73 views

Have to use pythagoras theorem

In parallelogram ABCD, the diagonals AC is at right angles to AB.If AB=12 & AC=13. I have to find the area of parallelogram. How can I use Pythagoras theorem here? I do not understand.
0
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1answer
71 views

Observations on integer-sided right triangles

Prove that in any integer side right angled triangle the following hold true: one side is always divisible by 3 one side is always divisible by 5 the product of two legs ...
0
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1answer
48 views

How to find the height of a 2D coordinate on a 3D triangle?

I would like to know how to dertermine the $Y$ coordinate of a point $M(X,Y,Z)$ in a triangle according to $MX$ and $MZ$, A,B,C ? Do I have to find the normal ? I have the coordinates of the points ...
0
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1answer
62 views

Using Barycentric coordinates to check whether a point lies within a Degenerate triangle

http://www.blackpawn.com/texts/pointinpoly/ I used this site to learn how to determine whether a point lies within a triangle. However, the site does not say whether or not this method can handle ...
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2answers
55 views

How do I find torque on an axis when no weight or force is given?

I need some help with the following problem: Find the torque around the x axis of the triangle with vertices (0, 0), (1, 4) and (1, 0). Assume the density equals one. — Life of Fred Calculus, ...
0
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1answer
71 views

The ratio of the area of $\triangle ABC$ to the length of $EF$?

In $\triangle ABC$, D is the foot of perpendicular from A on BC. If E and F are the feet of perpendiculars from D on AB and AC respectively, find the ratio of the area of $\triangle ABC$ to the length ...
0
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1answer
36 views

How do you determine if two triangles are intersecting for collision detection?

I've been scouring the internet for things about intersecting triangles. I haven't been able to find something that just gives me the math and what all the variables are equal to. I would love the ...
1
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1answer
35 views

Two inequalities in a triangle

I'm trying to prove that in a triangle with side lengths $a,b,c$, median lengths $m_a, m_b, m_c$ and circumdiameter $D$ the following inequality holds: $$ ...
1
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1answer
158 views

Geometry: Construct a rectangle with area equal to a given triangle and with one side equal to a given segment.

So we have triangle, ABC, and line segment DE. We don't know anything about them other than ABC is a triangle of some sort and DE is a line segment. We're tasked with constructing a rectangle such ...
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2answers
41 views

inequalites of an acute triangle angles $ 180^{180}*a^b*b^c*c^a \le (a^2+b^2+c^2)^{180} $

If $a,b,c$ are an acute angle of triangle the prove that $ 180^{180}*a^b*b^c*c^a \le (a^2+b^2+c^2)^{180} $ No idea
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2answers
32 views

Calculating two points on two different circumference of circle

Given the center point[(x1, y1), (x2, y2)], the radius(r1, r2), how to calculate the coordinate of two points on the circumference of circle? I have drawn a picture, the two points marked as red in ...
1
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1answer
76 views

How to find an angle of a non-right angle triangle when given two sides and an area?

How would I go about finding an angles of a non-right angled triangle when given the area and two of its sides. For example: In the triangle $ABC$, $a = 5$, $b = 6$ and the area is $11~\text{cm}^2$. ...
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2answers
46 views

Efficient way to check whether triangles are similar

If we need to find if a triangle is isosceles, we can compare like a=b, b=c and a=c. But there are 3 comparisons. With $(a-b)(b-c)(a-c) = 0$, we can check it with one comparison. Usually for similar ...
2
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2answers
113 views

Prove a length of 6 in a triangle diagram.

A puzzle: Three equilateral triangles of size 3, 4, and 7 touch at a corner. The other corners of the size 4 triangle are 3 away from a 3 corner, and 7 away from a 7 corner. How far apart are the ...
0
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1answer
162 views

Finding the angle of elevation, three points on ground know angles of two of them.

This would be a pain to clearly write out, so I've made a picture of the exact set up: I need to find the angle of elevation from point C. It's supposed to be $75^\circ$. I've tried using $\sin$, ...
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2answers
60 views

I need to prove that this line is a tangent to the circle

The problem is this: Given two different points, $A$ and $B$, take the midpoint between them ($O$) draw the circumference $\Gamma (O,OA)$ Take any point $C$ on $AB$ and draw a line $t$ perpendicular ...
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2answers
56 views

Linear algebra - find all possible positions of the third corner?

An equilateral triangle lies in the plane $x + y - z = 1$ and corners in points $(1, 1, 1)$ and $(2, 1, 2)$. Determine all possible positions of the third corner?
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1answer
72 views

How one can show Gerretsen's inequality?

I read from http://rgmia.org/papers/v6n3/wsh.pdf the following: A triangle with semiperimeter $s$, circumradius $R$ and inradius $r$ satisfies $$16Rr-5r^2\leq s^2\leq 4R^2+4Rr+3r^2.$$ How can I prove ...
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2answers
49 views

Trignometric inequality

if $\alpha, \beta, \gamma$ are angles of a triangle. prove that $\csc(\frac\alpha2)+\csc(\frac \beta2)+\csc(\frac \gamma2) \ge 6$. I started from $\alpha + \beta + \gamma = 180^{\circ}$ and then I ...
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3answers
59 views

Calculate the length of the sides of a triangle from the area and the angle

I need to find the length of the sides of a triangle. I have an angle and the area of the triangle. I have the answer but I don't know how to figure it out so it doesn't help. The area of the ...
0
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1answer
46 views

Finding Triangle's Angle

Find the value of $x$ if the area is $42\;\mathrm{cm}^2$. The triangle is not right angled or an isosceles. $X$ is the angle in the bottom left corner of the triangle that I need to find. The left ...
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2answers
64 views

Let $a,b,c$ be the lenghts of the sides of a triangle. Suppose that $ab+bc+ca=1$. Show that $(a+1)(b+1)(c+1)<4$

Let $a,b,c$ be the lenghts of the sides of a triangle. Suppose that $ab+bc+ca=1$. Show that $(a+1)(b+1)(c+1)<4$. My attempt: I tried multiplying the whole thing but that didn't help at all. ...
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2answers
42 views

Diagonal line through rectangle always creates two congruent triangles (?)

1) Is it true that the diagonal line through a rectangle always creates to congruent triangles? 2) If a quadrilateral has two right angles that are opposite (is this the right word to use), as ...
2
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4answers
87 views

In a triangle, prove that $a\cos A+b\cos B+c\cos C=\frac{8\Delta^2}{abc}$

I have to prove that for a triangle, $$a\cos A+b\cos B+c\cos C=\frac{8\Delta^2}{abc}$$ where $a,b,c$ are the lengths of the sides opposite to the angles A,B,C respectively. I followed the following ...