For questions about properties and applications of triangles

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3
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2answers
239 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 ...
3
votes
2answers
74 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
25 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 ...
1
vote
1answer
79 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 ...
1
vote
1answer
106 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 ratio $A:B$ is known. I want this mostly for personal ...
0
votes
0answers
538 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
votes
2answers
3k 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
votes
3answers
185 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
votes
2answers
29 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
votes
1answer
61 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
votes
2answers
299 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
votes
2answers
149 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
votes
2answers
148 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
3k 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
72 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 ...
2
votes
2answers
58 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
123 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
votes
4answers
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
vote
1answer
45 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( ...
1
vote
1answer
33 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: ...
1
vote
2answers
85 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
votes
1answer
118 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 ...
2
votes
2answers
51 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 $ABC$, ...
1
vote
4answers
73 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) $a^2+b^2=c^2=(x+y)^2=x^2+y^2+2xy$ $a^2=...
3
votes
2answers
95 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 problem?...
2
votes
2answers
58 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
votes
2answers
58 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
votes
1answer
43 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
votes
3answers
77 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
vote
1answer
76 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
votes
1answer
59 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
votes
2answers
63 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
votes
1answer
94 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. ...
3
votes
4answers
302 views

Triangle Inequality with Complex Numbers

I was wondering how to prove the triangle inequality with complex numbers: Verify that the function $d(z_1, z_2)$ is a distance funtion on $\mathbb{C}$ and also on any subdomain on $\mathbb{C}$. I ...
1
vote
1answer
229 views

The minimum perimeter and maximum height of a triangle under constraints

I'm developing a web application that consists of a calculator triangles. Although I am not a mathematician, with paper, derive and Geogebra I managed to get a lot of formulas to calculate a triangle ...
0
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1answer
39 views

Finding the lengths of this triangle?

please help, i'm to answer the question. The length of AB is 14.67106m. Please give working outs.
-1
votes
1answer
273 views

Geometry: Perimeter of triangle formed by intersections of tangents

I'm a bit stuck on the question below, and I wondered if anyone out here might be able to help: Construct a circle with a centre in O(0,0) and a radius of 5. Two tangents of the circle intersect in ...
0
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2answers
154 views

Hyperbolic Ideal Triangle

I have everything pretty much figured out everything but I need help proving the unique point formed by the three perpendiculars in the picture
0
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1answer
259 views

Finding the radius of excircles from a right angled triangle

Right angled triangles have 3 excircles, I'm struggling to find a formula which gives me the radius of all three excircles, I've been struggling with this for a while. I've done some googling and I ...
-1
votes
1answer
158 views

Generating a random num from a triangular distribution

http://en.wikipedia.org/wiki/Triangular_distribution#cite_note-1 under "Generating Triangular-distributed random variates" given that U is a number between 0 and 1, what happens if the a, b and c ...
1
vote
2answers
52 views

Find the acute angles of this right triangle.

I am having trouble finding the acute angles of this triangle. O is the intersection of the medians of the triangle and $OG = \frac{1}{2}OH$. Any suggestions?
1
vote
1answer
125 views

How to prove a triangle similarity problem

If I have a triangle $ABC$ with point $E$ lying on $BC$ and point $D$ lying on $AB$ where $AE$ is the height to $BC$ and $CD$ is the height to $AB$, how can I prove that triangle $ABC$ is similar to ...
10
votes
1answer
272 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 ...
2
votes
0answers
28 views

Statue and a flag distances

Next to a flagpole is a statue that measures 9m high. The upper end of the flagpole with the bottom of the statue form an angle of 53.13 degrees to the floor, and the upper end of the flagpole to the ...
1
vote
3answers
171 views

Why are trig functions defined for the unit circle?

Why did we ever need to define the trig functions of angles greater than 90 degrees or less than 0 degrees? What is the use of applying trig functions to such angles? If we apply the trig functions ...
0
votes
1answer
46 views

Finding the angle?

I have two circles which share a radius of R units, and each circle contains the center of the other circle. I found that the area of the segment would be, $\theta$ is the central angle between the ...
-1
votes
2answers
448 views

Incenter divide ratio

Given a triangle $ABC$ and angle bisectors $BD,CE$ which intersect at $O$ (incenter) . The ratio in which $O$ divides $BD$ is $3:2$ and it divides $CE$ in ratio $1:2$ . Find the ratio in which the ...
6
votes
2answers
138 views

The conjecture that no triangle has rational sides, medians and altitudes

I have found a conjecture that there is no triangle whose sides, medians, altitudes and area are all rational. I figure that someone must have already found such a triangle if one existed and yet I ...
1
vote
1answer
36 views

How many ways are there to break up the regular 9-gon into triangles by diagonals?

How many ways are there to break up the regular 9-gon into triangles by diagonals? UPD Guaranteed to be convex - yes. Intersecting "diagonals" be allowed - yes. 2nd UPD It is task for programming ...
0
votes
2answers
43 views

Right angled triangle log

If $a,b$ and $c$($c$ is the hypotenuse) are sides of a right triangle then prove $$(\log_{c+b}a)+(\log_{c-b}a)=2(\log_{c+b} a )\cdot(\log_{c-b}a)$$ The bases are different so can't quite figure out ...