For questions about properties and applications of triangles

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2
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1answer
70 views

find parameter for maximize area

suppose that we have Cartesian coordinate system.and suppose that we have three point which depend on parameter $t$,where t belongs to $(0,1)$;points are $A(cos(3-t),sin(3-t))$ $B(cos(t),sin(t))$ ...
1
vote
2answers
92 views

find angle in triangle

Let us consider problem number 21 in the following link http://www.naec.ge/images/doc/EXAMS/math_2013_ver_1_web.pdf It is from georgian national exam, it is written (ამოცანა 21), where word ...
1
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4answers
164 views

Where does $\sin 3° =3\sin 1° -4 \sin^3 1°$ come from?

Wikipedia makes the claim: "Though a complex task, the analytical expression of $\sin 1°$ can be obtained by analytically solving the cubic equation $\sin 3° =3\sin 1° -4 \sin^3 1°$ from whose ...
4
votes
2answers
225 views

$x \sin x=2$ why is my proof that there no solutions wrong?

$\frac 12 x \sin x=1$ . Let's look at a right triangle with base $x$ and altitude $\sin x$ . Then our equation is for the area of this triangle. Let the sides of the triangle be $a=x$ , $b=\sqrt ...
0
votes
1answer
47 views

Modification of the triangle inequality

We know from the triangle inequality that $X+Y \geq Z$, My question is under what conditions of $a,b,c$ (acute, obtuse or right angle) that $Z >X $ and $Z \geq Y $
2
votes
1answer
506 views

Move Point A along a line

Sorry, can't post images if my rep is below 10, and can't post more than 2 links. I removed the http section so it won't count as a link. I hope this isn't against forum rules, I'm not hurting anyone. ...
0
votes
2answers
286 views

Split a triangle into two right triangles

Lets assume I have a triangle $(p0, p1, p2)$ with $(p1 - p0)$ the longest edge. I am looking to find the point $q$ on the edge $(p1 - p0)$ such that $dot(p2 - q, p1 - p0) = 0$. That is to say; the ...
0
votes
1answer
77 views

Get Normal of a 3D point.

I have set of points. I created strip triangles using these points. Now I need to calculate normal. What I thought that for each triangle there should be a normal. But function I am using says that ...
3
votes
4answers
80 views

Limit on the expression containing sides of a triangle

To find the bounds of the expression $\frac{(a+b+c)^2}{ab+bc+ca}$, when a ,b, c are the sides of the triangle. I could disintegrate the given expression as $$\dfrac{a^2+b^2+c^2}{ab+bc+ca} + 2$$ and ...
0
votes
5answers
83 views

How to I find the length of a side on a triangle?

how do I find line AB in this if ac is 6cm, and bc is 14cm? angle A is 59*, c is 55*, and C is 66*. (not to scale) thanks in advance
2
votes
1answer
2k views

What's the ratio of triangles made by diagonals of a trapezoid/trapezium?

In the above image, what will be the ratio of areas of triangle $A$ and $B$? From Googling, I've found that: $\operatorname{Ar}(A) = \dfrac{a^2h}{2(a+b)}$ and $\operatorname{Ar}(B) = ...
0
votes
1answer
75 views

Radius of in-circle as a function of the center

I am trying to find the radius of an in-circle in a random triangle as a function of the center of the circle. Let (x,y) in\R^2 be the center of a circle, r the radius then i need an expression of the ...
0
votes
1answer
80 views

Tangent of circumscribed circle

I found a solution online which it said : "It's easy noted that $AG.AE$ = $AD^2$ = $AF^2$ (Using tangent of circumscribed circle)" I found this not obvious at all. I know that $AD = AF$ but why it ...
1
vote
1answer
571 views

Zero “norm” properties

I have seen the claim that the l0-norm ($\|X\|_0$ = support(X)) is a pseudo-norm because it does not satisfy all properties of a norm. I thought it to be triangle inequality, but am not able to show ...
1
vote
2answers
251 views

Does this proof work to prove that the greatest area of a triangle inside a circle is when the triangle is equilateral?

Does this proof work to prove that the greatest area of a triangle inside a circle is when the triangle is equilateral? I gather it doesn't because most of the proofs I've seen use derivatives etc. If ...
0
votes
1answer
53 views

Trigonometry problem, using COS

Let's say two right angled triangles share a common hypotenuse which measures 10 in length and share an angle which measures $20^\circ$ in total. How do I work out the value of x (the side adjacent to ...
0
votes
0answers
115 views

Line Triangle Intersection Mathematics

I am following the math in the book Real Time Collision Detection by Christer Ericson. On pages 184 thru 188, he discusses how to test for an intersecting line against a triangle. I replicated the ...
1
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3answers
143 views

Right Triangle Trig

I need to find the measure of each angle indicated and round to the nearest tenth. I am given two sides 12 and 13 and one angle C which is 90 degrees. How do I figure this out?
1
vote
3answers
867 views

Triangle inscribed in circle, vertex at circle's center, solve for unknown angles.

$O$ is the center of the circle , $A$ and $B$ lie on the circle what are the possible values of $x$ and $y$ I found answers options , asked to mark one or more ...
1
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3answers
82 views

Find coordinates of vertex of equilateral triangle

$ABC$ is an equilateral triangle , $AC = 2 $ What is the value of $p$ and $q$ ?
19
votes
1answer
734 views

Are there prime lengths in triangle with all integer sides and heights?

Suppose you have a triangle in which all sides and all heights are integer in length (i.e. triangle with sides 20, 25, 15 has heights 15, 12 and 20). Could it be that at least one of those numbers is ...
0
votes
1answer
60 views

is there a formula for working out the angles of a triangle to make the sides meet at the top?

I am doing a GCSE maths foundation paper for revision and one question has a triangle with the base side being 9cm and the other 2 sides 7.5cm. Is there a formula for finding the angles of the ...
1
vote
2answers
101 views

Minimizing area of a triangle with two fixed point and a point on parabola

A triangle is made up of three points, $A, B$, and $P$. $A(-1, 0)$ $B(0, 1)$ $P$ is a point on $y^2 = x$ Minimize the area of Triangle $ABP$. My approach is far too complicated, which ...
7
votes
1answer
1k views

Sum of distances from triangle vertices to interior point is less than perimeter?

Let $M$ be a point in the interior of triangle $ABC$ in the plane. Prove $AM+BM+CM<AB+BC+CA$. The above question was posed to someone I know who is taking high-school Euclidean geometry. I'm ...
4
votes
4answers
5k views

Find the legs of isosceles triangle, given only the base

Is it possible to find the legs of isosceles triangle, given only the base length? I think that the info is insufficient. Am I right?
2
votes
1answer
59 views

Find the value of the expression $\frac{AF}{FD}$.

In the given figure $AC=BD=3$ units and $CE=DE=1$ unit. Find the value of the expression $\frac{AF}{FD}$. We know that the median divides the area of a triangle in to two equal halves. Therefore, ...
0
votes
2answers
199 views

Sides of the Right angled Triangle in Complex notation.

If $z=a+ib$ is a complex number, then $z, iz, z+iz$ represents sides of the right angled triangle. I got this result through Cartesian form, i,e. $(a,b),(-b,a) and (a-b,a+b)$ are the vertices of the ...
3
votes
1answer
356 views

Algorithm to find rectangle inside a triangle

I am trying to write a program that generate procedural cities. However, I am stuck on a problem : I don't know how to subdivide a triangle into a rectangle and other triangles. I know how to ...
5
votes
2answers
527 views

When is the area of a triangle whose side lengths are consecutive integers also an integer?

Consider a triangle with side lengths 3, 4, and 5. By Heron's formula, its area is $\sqrt{6(6 - 5)(6-4)(6 - 3)} = \sqrt{6(1)(2)(3)} = \sqrt{36} = 6$. Are there any other triangles like this?
0
votes
1answer
150 views

Drawing a triangle in a unit circle

This is a question that I derived for a long time ago. It asks if we draw a triangle in a unit circle does all arc lengths $(\alpha ,\beta ,\theta)$ and sides of triangle $(a,b,c)$ can be rational ...
1
vote
1answer
114 views

Need help solving -

i was writing an paper on solutions of triangles when i encountered this sum - In a $\Delta$ ABC , P is an interior point such that $\angle PAB = 10^\circ$ , $\angle PBA = 20^\circ$ , $\angle PCA = ...
0
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3answers
106 views

Similar triangles question

If I have a right triangle with sides $a$.$b$, and $c$ with $a$ being the hypotenuse and another right triangle with sides $d$, $e$, and $f$ with $d$ being the hypotenuse and $d$ has a length $x$ ...
2
votes
5answers
161 views

How can I solve this Laws of Sines problem?

This is a homework question that was set by my teacher, but it's to see the topic our class should go over in revision, etc. I have calculated $AB$ to be 5.26m for part (a). I simply used the law ...
2
votes
1answer
113 views

Property of bisectors of right triangle

In triangle $ABC$ $\angle C=90^\circ$, $AA'$ and $BB'$ are angle bisectors intersecting at $I$ ($A'\in BC$, $B'\in AC$). What would be the easiest way to prove that projection of $I$ onto $AB$ lies in ...
6
votes
4answers
2k views

How to find area of triangle from its medians

The length of three medians of a triangle are $9$,$12$ and $15$cm.The area (in sq. cm) of the triangle is a) $48$ b) $144$ c) $24$ d) $72$ I don't want whole solution just give me the hint how ...
0
votes
1answer
64 views

find area of Triangle ABF

In the figure given below, rectangle $CDEF$ with perimeter $32$ has the maximum area. Find the area of the triangle $ABF$ So, I tried the following $P = 2W+2H$ where $P$ is given $32$. I am not ...
-1
votes
2answers
133 views

Find area of triangle ABC

BD Perpendicular AC , AB =BC=a Find the area of triangle ABC I have tried Googling , I used formula 1/2 (base X Height) . Used Pythagorean theorem. Anyone can suggest me solution.
2
votes
3answers
412 views

Geometry - Equilateral triangle covered with five circles

I have to cover an equilateral triangle (whose sides are 1m long) with 5 identical circles: what's the minimum radius of the circles?
2
votes
4answers
262 views

Length of Triangle BCD

Hey, well I'm doing some higher level revision and I'm stuck... In the diagram triangle BCD is mathematically similar to triangle ACE. So what is the length of BD? How do you work it out?
2
votes
1answer
51 views

point on triangle

let we have a domain, for example square that partitioned by some triangles that are not necessarily similar, and we know the coordinates of all vertices and the maximum size of the sides of all ...
1
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2answers
254 views

Can all possible angles on a rational triangle be represented as a rational multiplied by Pi?

The reason I ask: I was wondering if it was possible to find the angle of a rational triangle by only using the lengths of its sides and knowledge of $\pi$ (that is, no inverse trig functions). So, ...
0
votes
1answer
41 views

a question about triangle

Let $(x_1,y_1),(x_2,y_2),(x_2,y_2)$ are the vertices of the triangle T. I want to show that the line $L(\alpha_3)$ defined by $$x=(1-\alpha_3-\alpha)x_1+\alpha x_2+\alpha_3 x_3$$ ...
1
vote
0answers
113 views

Proving that the circumcenter is the centroid

Given a triangle and its centroid, we know that the 3 line segments between the centroid and each of the vertices of the triangle divide the triangle into three smaller triangles. Prove that the ...
0
votes
1answer
73 views

To find a point in a horizontal plane to minimise the distance

A, B and C are three points in 3D space. The points A and B are fixed. C is below A and B. $H_{p}$ is any given plane. Point C moves along the plane $H_{p}$. How to find the location of point C ...
1
vote
0answers
83 views

maximum length of a scaled vector in a triangle (simplex)

Given a triangle (or, in general, a simplex) $T$ and a vector $\vec{s}$, I'd like to compute the quantity $$ \max\{|x-y|: x,y\in T, x-y = \alpha \vec{s}, \alpha\in\mathbb{R}\} $$ i.e., the maximum ...
1
vote
1answer
148 views

Triangle optimization problem

Let $a,b,c$ be the sides of a triangle , then what is the maximum and minimum values (if exist) of the following quantities (i) $\dfrac {a^2b^2c^2}{(a+2b)(a+2c)(b+2c)(b+2a)(c+2a)(c+2b)}$ (ii) ...
0
votes
3answers
3k views

Calculating circle radius from two points and arc length

For a simulation I want to convert between different kind of set point profiles with one being set points based on steering angles and one being based on circle radius. I have 2 way points the ...
2
votes
1answer
74 views

Angle sum of a triangle.

Can you please describe the geometry in which the sum of the angles of the triangle can be less than 180 degrees?
0
votes
2answers
22 views

Triangle inequlity improvment with the angle conditions

I was working on how to proof $a+b \leq x+y+z$? Apply triangle inequity to the triangle ADC, $x+z \geq a$ Apply triangle inequity to the triangle DCB, $y+b \geq z$ Adding above inequities, ...
1
vote
1answer
82 views

P is a point in triangle $ABC$, what is $[APC]$?

Moderator Note: This question is part of an ongoing contest on Brilliant.org, and will be unlocked in 1 week. P is a point in triangle $ABC$. The lines $AP$,$BP$, and $CP$ intersect the sides ...