For questions about properties and applications of triangles

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0
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1answer
116 views

Angle between two rectangles rotated around a point with a gap inbetween

I am trying to find the angle between two rectangles when there is a known gap between them. See this diagram: I have simplified the problem into three triangles, two of which are the same. Here ...
3
votes
1answer
88 views

Möbius Transformation of Triangles

I understand that Möbius transformations are angle preserving transformations. Knowing this, my professor asked us to think about how the image of equilateral triangle is not an equilateral triangle ...
1
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1answer
71 views

Number of ways to form isosceles triangle by picking points on a circle

Given a circle with 24 evenly spaced points, how would you find the number of possible isosceles triangles (which includes equilateral) that can by drawn using the points? My attempt was to say that ...
5
votes
1answer
94 views

Prove that $\|a\|+\|b\| + \|c\| + \|a+b+c\| \geq \|a+b\| + \|b+c\| + \|c +a\|$ in the plane.

Prove that $\|a\| + \|b\| + \|c\| + \|a+b+c\| \geq \|a+b\| + \|b+c\| + \|c +a\|$ in the plane. Gentle hints only, please! I know that attempting to decompose R.H.S. into $$\alpha a + \beta b + ...
3
votes
1answer
628 views

Solving circle's radius only knowing angle & lengths of external triangle OR solving for sides of a triangle partial side lengths

Is this possible? Given that I know the length of Y and Z and the angle of X can I figure out the radius A? If I can't without more information, I can produce another set of data X Y Z at a ...
1
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3answers
1k views

Minimum distance between point and face

Given a point in 3D space of the form (x, y, z) and a triangle consisting of 3 vectors (also in the (x, y, z) format), how would I calculate the minimum distance between the point and the face of the ...
1
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0answers
232 views

Question on Proof of Shoelace Formula

I was looking for a way to prove the shoelace formula when I found this proof: For this clockwise order to make sense, you need a point O inside the polygon so that the angles form $OA_{i}A_{i+1}$ ...
0
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1answer
49 views

$3x+3y-1,4x^2+y-5,4x+2y$ are sides of an equilateral triangle

I am completely lost in this one $3x+3y-1,4x^2+y-5,4x+2y$ are sides of an equilateral triangle, its area is closest to the which integer?
0
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2answers
216 views

$m$ be the number of distinct non congruent integer sided triangles each with perimeter $15$

Let $m$ be the number of distinct non congruent integer sided triangles each with perimeter $15$ and $n$ be the number of distinct non congruent integer sided triangles each with perimeter $16$ Then ...
1
vote
1answer
288 views

Finding the interior angle between two lines of slopes $m_1$ and $m_2$ from a programming perspective

I have been working on a 2-dimensional object creator program that handles manipulations of arbitrary shapes and calculates collision detection between them. The program allows you to input a shape's ...
2
votes
1answer
78 views

Where am I wrong in finding area of this triangle?

I was self-reading Mathematics for Economists by Simon and Blume. On page 815, Section 29.4, he has discussed "Norms on Function Space". And here I am stuck: Let $$f_n = \begin{cases} 2n^2-2n^3x, ...
0
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1answer
163 views

Area of triangle $OAB$

Question is : Consider a circle of unit radius centered at $O$ in the plane. let $AB$ be a chord which makes an angle $\theta$ with the tangent to the circle at $A$ .find the area of triangle $OAB$ ...
0
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1answer
115 views

finding the area of triangle

its an 8th standard question . but i m unable to solve it. please help Question " the perimeter of a triangle is 84m . the sides are in the ration 13:14:15 . find the area . " (answer should come ...
2
votes
3answers
91 views

Area of a critical Triangle

help me to solve this this problem please: In a triangle $ABC$, $\angle BAC$ = $60\,^{\circ}$,$AB=2AC$.Point P is inside the triangle such that $PA=\sqrt{3}$,$PB=5$. What is the area of triangle $ABC ...
0
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1answer
100 views

triangle inequality given perimeter and area

Show that the following inequality holds between the perimeter $p$ and the area of the triangle $a$. $$p^2 \ge 12\sqrt3\ a$$
2
votes
1answer
118 views

Find length of triangle side

There is a triangle $ABC$ where $|CB|=a$, $|AC|=b$ and medians of these sides intersect at a right angle. Find |AB|. I don't know how to use a right angle in this problem. I have a idea to link a ...
3
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3answers
167 views

Find out the angle of <ABC

Help me to solve it please.how could it be done.I tried but nothing comes out.Help me please
2
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1answer
493 views

Korean Math Olympiad 1993 (geometry)

Consider a $\triangle ABC$ with $BC = a$, $CA = b$, $AB = c$. Let $D$ be the midpoint of $BC$ and $E$ be the intersection of the bisector of $A$ with $BC$. The circle through $A$, $D$, $E$ meets $AC$, ...
2
votes
1answer
138 views

Triangle Ratio/Proportions Problem

I would like someone to verify that I am solving this problem correctly. I do not remember the theorem that allows me to make the two halves of the triangle proportional. Because (h1/h2 = h1/h2) ...
4
votes
1answer
296 views

Triangle ratio of areas

This is a photo that was originally posted on Google Plus. I would like to know how to solve for S. I started by splitting S into two parts S1 and S2 by drawing a line from A to M. I also know that ...
0
votes
2answers
46 views

How does this proof of law of sines determine equal angles?

I was reading over this proof of the law of sines and they say that $\angle CAB = \angle DOB$ because of "basic geometry". I do not get it though, how can you say that the angles are equal?
0
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2answers
391 views

Equations of triangle sides through medians

This has been bothering me for a while. Given a vertex $A(2;-4)$ and the line equations of two medians ($2x-3y-2=0$ and $5x+3y-12=0$), find the line equations on which the triangle sides are. I've ...
4
votes
1answer
166 views

Is it possible to approximate all angles with certain pythagorean triples?

With sticks $a,b$ and $c$ of length $3,4$ and $5$, you able to draw a right (tri)angle. But are also able to construct an angle $\cos\alpha=\frac35, \alpha=\arccos(\frac35)=$$53.13010...^°$. Is it ...
3
votes
1answer
94 views

Area of a rhombus

$ABCD$ is a rhombus. We are given the the circumradius of triangles $ABD$ and $ACD$. So how do we compute the area and the side and area of the rhombus? I have tried some properties of the ...
1
vote
3answers
16k views

In a right triangle, given slope and length of hypotenuse find length of legs.

Say I have a right triangle. I know the slope and length of $c$, how do I find the length of $a$ and $b$?
1
vote
1answer
85 views

Nine-point-circle, midpoint of triangle

ABC is the triangle and M, N are midpoints of AB and AC. Points W, X are on AB, Y, Z are on AC such that WM = MX, ZN = NY. Let T be the intersection of WY and XZ, prove that T lies on the nine point ...
5
votes
2answers
2k views

Proof for SSS Congruence?

I'm hoping that someone can provide a method for deducing the commonly known SSS congruence postulate? The postulate states If the three sides of one triangle are pair-wise congruent to the three ...
1
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0answers
44 views

Largest possible value of a side

ABC is a triangle with side a, b,c with $a\geq b\geq c$ and $sin^3A+sin^3 B+ sin^3 C=a^3+b^3 +c^3$ How do I find the largest possible value of a? I tried to use the law of sines ratio, but it ...
0
votes
1answer
4k views

Ratio of angles in a triangle, given lengths of triangle's sides.

If I have a triangle $\,\triangle ABC,\,$ with sides of lengths $\,AB=6, \;BC=4, \;CA=5,\,$ then what can I know about the ratio of $\,\dfrac{\angle ACB}{\angle BAC}\,$?
0
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2answers
48 views

Problem with finding “x” in triangle

I have got a problem with finding the x. I think the question isn't true or there should more informations on it.
3
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1answer
397 views

In Triangle ABC , BM and CN are perpendiculars from points B and C on any line passing through A. If L is the mid-point of BC, prove that ML = NL

I found this question in my textbook and I think this question requires the use of the mid-point theorem. I even tried proving the equality using congruence but couldn't seem to make a headway. I am ...
1
vote
1answer
27 views

How to maximize the function

I have a triangle $T=ABC$. I want to calculate $\max (a-b)$, where the the angle $ABC = \beta$, and $|AB|=c$ is fixed (pre-known). My guess is $c\times\cos (\beta)$, but I want to prove it. Let ...
0
votes
2answers
749 views

How to calculate the angle between two vectors, defined by 3 points on the earth?

I want to develop a formula to calculate the angle between two vectors. The vectors will be OX and OY (from point O to X , and Y), where the points are defined by their latitude and longitude values. ...
0
votes
1answer
331 views

What is a generic triangle?

I think the question speaks for itself. I came across this term in one exercise, but am not sure what it is. The definition my textbook gives is a triangle where the three vertices are free. I am ...
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2answers
84 views

Proof using properties of an isosceles or right-angle triangle

Given a $\triangle ABC$ with sides $AB=BC$ and $\angle B=100^\circ $, prove that $$a^3 + b^3 = 3a^2b$$ where $a=AB=BC$ and $b=AC$, I have tried to use simultaneously the sine and cosine rules as ...
2
votes
1answer
4k views

Find height of a triangle given length of three sides?

How can I find the height of a triangle given the length of all three sides? The only solution I could find was to use Heron's formula to find area then $A=\frac{1}{2}bh$ to find height. Is there an ...
2
votes
0answers
85 views

Minimize the perimiter of a triangle with an inscribed circle

A circle touches the two legs of an angle. How can one draw a line that intersects both legs, such that the circle lies within the triangle with as sides the two legs and the drawn line, and such that ...
1
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0answers
66 views

Probability of a triangle in a circle [duplicate]

I'm confused on my calculations on analytic geometry with probability. Things I learned on these were messed up since I was a newbie on these subjects. Here's my problem: Three points are chosen ...
3
votes
1answer
112 views

Inequality in triangle

Let $ABC$ be a triangle and $M$ a point on side $BC$. Denote $\alpha=\angle BAM$, $\beta=\angle CAM$. Is the following inequality true? $$\sin \alpha \cdot (AM-AC)+\sin \beta \cdot (AM-AB) \leq 0.$$
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2answers
125 views

Finding the measurement of an angle

I have been stumped on this problem for a couple days now, and I would like some help solving it. Here is the picture that I drew up: $ABCD$ is a regular square. Line $FG$ is a perpendicular ...
0
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2answers
3k views

What is the maximum area of a square inscribed in an equilateral triangle?

What is the maximum area of a square inscribed in an equilateral triangle? Please post the approach to solve the above question.
2
votes
1answer
146 views

Prove, square of quadrilateral is the sum of squares of 4 triangles [duplicate]

Let $A_1$, $B_1$, $C_1$, and $D_1$ - midpoints of the sides $AB$, $BC$, $CD$ and $DA$ convex quadrilateral $AВСD$. Directs $AC_1$, $ВD_1$, $CA_1$ and $DВ_1$ - divide it by $5$ quadrilaterals and $4$ ...
0
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1answer
1k views

Determine if projection of 3D point onto plane is within a triangle

In 3D, given three points $P_1$, $P_2$, and $P_3$ spanning a non-degenerate triangle $T$. How to determine if the projection of a point $P$ onto the plane of $T$ lies within $T$?
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5answers
8k views

Is there any equation for triangle?

Like there's an equation of a circle, is there any equation of a triangle? I've been trying to build one and the closest thing I've managed to do is to create an equation of 2 lines and use the $x$ ...
1
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2answers
397 views

In an equilateral triangle what is sum of distance from vertices to a point inside the triangle?

In an equilateral triangle what is sum of distance from vertices to any arbitrary point inside the triangle? What is the relation between $a$ and $x + y +z$. The special condition is that the ...
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0answers
42 views

Trigonometry: Isosceles Triangle [duplicate]

I saw the following problem on Facebook (figure not drawn to scale): ...
1
vote
5answers
137 views

Right Triangles and Altitudes

I am once again stuck on a question about geometry, this problem is about altitudes that crate right triangles: Let there be a triangle that has side lengths of 13, 20, and 21. Given this, find the ...
2
votes
1answer
77 views

Finding inradius given the heights

I'm given the heights of a triangle. Find the inradius. I know that inradius is area/semiperimeter. But then?
2
votes
3answers
1k views

Proving the length of angle bisector

How do I prove that a triangle with sides a, b, c, has an angle bisector (bisecting angle A) is of length: $$\frac{2 \sqrt{bcs(s-a)}}{b+c}$$ I have tried using the sine and cosine rule but have ...
3
votes
1answer
586 views

Triangle Point Picking in 3D

To take random uniform points inside a triangle Triangle Point Picking method is used. But this is for 2D points, how can I take random points from a triangle that is defined by 3 arbitrary 3D points? ...