For questions about properties and applications of triangles

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2
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1answer
29 views

What are the angles of a triangle which shares points with a regular pentagon adjacent to a square? [Image]

My cousin had a geometry homework question, which asked to find the angles of a triangle inside the following shape That was fairly simple. (The angles are 45, 54, and 81 degrees because both are ...
1
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1answer
42 views

Sierpinski Triangle Applications

Sierpinski triangles seem to be a pretty common fractal. After lots of searching, I can't seem to find where you find this pattern in nature or technology. Are there any examples in nature? What about ...
1
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1answer
69 views

Proof of converse of Menelaus's Theorem

I am not understanding completely the last affermation of the following proof of the converse of Menelaus's Theorem. In the detail, the author, after having proven in general Menelaus's Theorem for ...
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1answer
30 views

Find the coordinats of a triangle after rotation [closed]

How to calculate new coordinate of a 2d triangle rotated by Q degrees? We confused that x = old X - center of mass X y = old Y - center of mass Y x = x * cos(Q) - y * sin(Q) y = x * sin(Q) + y * ...
2
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1answer
26 views

How to proof that those triangles are similar?

I have given that : The triangle ABC Isosceles triangle(AC = BC) The angle at the base is 72 degrees There is a bisector L for the angle A I have to proof that ...
4
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2answers
56 views

Can I square the triangle?

I know I can't construct a square with the same area as a given circle (because $\pi$ is transcendental). Can I construct (ruler and compass) a square with the same area as a given triangle? I think ...
2
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4answers
81 views

Prove that the triangle is isosceles, based on the intersection of two line segments connecting vertices to sides [closed]

Given $AB=AC$ and $DE=DF$, prove $DB=DC$ I have no idea how to solve it using elementary way, can somebody help me?
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0answers
22 views

Triangle Inequality for vector spaces

Consider the triangle ABC and suppose that the lengths ∥AB∥ and ∥AC∥ of the directed ⃗⃗ line segments AB and AC are 2 and 3, respectively. What one concludes about the length ⃗⃗ ∥BC∥ of BC? ...
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1answer
47 views

Inscribe circle in triangle

In a triangle $ABC$ a point $I$ is a centre of inscribed circle. A line $AI$ meets a side $BC$ in a point $D$ . A bisector of $AD$ meets lines $BI$ and $CI$ respectively in a points $P$ and $Q$. ...
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1answer
39 views

proving an inequality of sides of a triangle with trigonometry.

On a textbook I was working with there was this question: When $a,b,c$ are the three sides of a triangle, prove that $a^2+b^2\gt\frac{c^2}{2}$ Since $(a-b)^2\ge0$, $a^2+b^2 \ge 2ab$, and ...
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0answers
28 views

ABC is an acute angled scalene triangle.L,M,N are midpoints of the sidesBC,CA,AB.The perpendicular bisectors of AB and CA meet AL at D and E.

BD and CE cut each other at F inside the triangle.Prove that A,M,N,F are cyclic. I tried by taking a point on symmedian and also ...
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0answers
61 views

Triangle bisector length problem

I had this task on my math test: In the triangle ABC, the bisector of angle at C intersects side AB at point D. Given that the angle at C is 120°, |AB| = 6cm and |BC| = 12cm, calculate the length of ...
0
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2answers
28 views

Equilateral triangle on the argand diagram

Let $P=3+2i$ be a point in the plane. Find points $Q$ and $R$ such that $PQR$ form an equilateral triangle with the center (of the triangle) at the origin. Does anyone know what to do?
2
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2answers
24 views

Product of inscribed circle and circumscribed circle radiuses [closed]

Let a and b be the two shortest sides of a triangle. r is the radius of the inscribed ...
0
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2answers
42 views

How do you explain the sine function of a basic triangle wave?

I am working on an investigation focusing on mathematics in music. Modelling various different chords and their mathematical functions, I now need to understand (in relative detail) how the most basic ...
0
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1answer
34 views

Solving geometric problem

I want to find the coordinates of the $p$ point and $\beta$ angle in the following figure. The point is defined by the angle $\alpha$, the positions of the $a$ point, and the radius of the circle $r$, ...
0
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1answer
21 views

Triangle and parallel lines

L1 and l2 are parallel how can I find the angle of x , y , z ?
2
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2answers
59 views

area of a right angled isosceles triangle.

Given the base of an isosceles right angle triangle is $30$ cm.It is required to find the area of the same. Its quite clear that if the triangle is isosceles right angled triangle, and its base is ...
1
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1answer
36 views

Find the cosine of angle $A$ if the sides of triangle $ABC$ are related as $3:2:2$.

So it has been a while since I last studied Trigonometry, so I thought I should revise it and solve on it. So I was solving on Cosine/Sine laws and I came across this question that I really couldn't ...
3
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1answer
30 views

Proving perpendicularity

Let $ABC$ be a triangle. Let $I$ be its inscribed circles' center. Let $D$ be the intersection point of lines $AI$ and $BC$. The perpendicular bisector of $AD$ intersects with $BI$ in $E$. Thesis: $$ ...
0
votes
1answer
73 views

How do I construct a 4 sided 45 degree pyramid from four triangular planes ( open on bottom )

I have two square mirrors, and I'm trying yo create a four sided 45 degree pyramid with as few cuts as possible. I'm trying to figure out how to design a 2d pattern that will result in the pyramid I ...
0
votes
1answer
23 views

How to determine if two vectors intersect in 3D space

I have two triangles in 3D space with a shared edge. I need to determine if the triangles exist on the same plane. To do this, I need to determine if the vector between the unshared points (P1 -> ...
0
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1answer
33 views

How to find the inradius of orthic triangle?

How to find the inradius of orthic triangle in terms of side lengths or area or circumdiameter of original triangle? The incentre of the orthic triangle is the orthocentre of the original triangle. ...
2
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5answers
98 views

Find the area of the triangle

There are two points $N$ and $M$ on the sides $AB$ and $BC$ of the triangle $ABC$ respectively. The lines $AM$ and $CN$ intersect at point $P$. Find the area of the triangle $ABC$, if areas of ...
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2answers
30 views

Similarity Ratios in triangle

Triangle $ABC$ is given. Let $M$ and $N$ be points on its sides $BC$ and $AC$ respectively, such that $BM/MC$ = $1/3$ and $AN/NC$ = $1/5$. If $O$ is the intersection point of $AM$ and $BN$, find ...
0
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1answer
85 views

How to calculate the projection of a side in a triangle

Given the following triangle, with the vertices $P, +q, -q$ why is $r_2 - r_1$ the projection of the side $-q+q$ on the side $-qP$? Thanks a lot !
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3answers
45 views

Disproving $A-S-S(Angle-Side-Side)$ congruence condition…

I know that $A-S-S$$(Angle-Side-Side)$ congruence does not exist.But I cannot disprove it. Every time I draw a figure,I get two congruent triangles. My Attempt- So,we draw two lines such that ...
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1answer
36 views

Triangle whose corners are N(0,1) variables

A friend of mine and I have been exchanging and solving math puzzles and this is the last one: A triangle is formed by three points on a plane, whose $x$ and $y$ coordinates are $N(0,1)$ random ...
0
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1answer
26 views

How can I determine the sides in a squished hexagon?

How can I determine the sides, and the angle with horizontal, in a squished hexagon ? If I start with a regular hexagon (coordinates (75,0); (25,0); (0, 50*sin60);(25,100*sin60); (75,100*sin60); ...
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3answers
87 views

To find ratio of Length and Breadth of a Rectangle [closed]

Given a rectangular paper sheet. The diagonal vertices of the sheet are brought together and folded so that a line (mark) is formed on the sheet. If this mark length is same as the length of the ...
0
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1answer
30 views

Set of all contraction maps

Consider $(X, d)$ be a compact metric space, and let $Con(X)$ denote the set of all contraction maps on $X$. We shall define the “distance” between two maps $f, g ∈ Con(X)$ as follows, $$d_{Con(X)}(f, ...
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1answer
32 views

Find a shape that fits inside a box, given it may be drawn with thick pen

I have to draw a regular shape, that fits inside a rectangle of given size. The pen used to draw that shape follows the shape I say it is - going from corner to corner - but the pen thickness is ...
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0answers
55 views

Proof of the Crossbar theorem

A teacher asked me to prove the well known Crossbar theorem. I tried it in the following way:- Given: If $D$ is in the interior of $\triangle ABC$, then prove that $\overrightarrow{AD}$ intersects ...
2
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1answer
45 views

Problem relating to ratios and escribed circles

If $I_1$ and $I_2$ and $I_3$ be the centres of the escribed circles of $\triangle ABC$ and if $R_1$, $R_2$ and $R_3$ are radius of the circles inscribed in the triangles $\triangle BI_1C , \triangle ...
0
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1answer
72 views

How do I find the altitude, base and the length of a triangle?

The base of an Isosceles triangle is $5\text{ cm}$ longer than the height. If the area of the triangle is $12\text{ cm}^2$. Find the height, base and the length of one of its equal sides.
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0answers
22 views

Quadrilateral inside a Parallelogram

$ABCD$ is a parallelogram with diagonal $AC$. $BE$ is the median to side $CD$ ,intersecting $AC$ at $O$.If the area of $ABCD$ is $120$ units, find the number of square units in the areas of ...
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1answer
71 views

Intersection point and angle between the extended hypotenuses of two right-angled triangles in the plane

The end points of two line segments (the hypotenuses of red and blue right-angled triangles below) are given below with their coordinates marked separately on the $x$- and $y$-axes. These points are ...
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3answers
203 views

Question related to tan in a ratio in a triangle

If in a triangle $\tan A:\tan B:\tan C = 1:2:3$ then, what are the ratio of the sides $a,b,c $?
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2answers
41 views

How to prove this inequality (like triangle inequality)

[Question] $$ \left|\sqrt {x^2+y^2}-\sqrt {x^2+z^2}\right| \le |y-z| $$ [My Effort] $$ \begin{align} &I_1=\sqrt {x^2+y^2} \le |x|+|y|\\ &I_2=\sqrt {x^2+z^2} \ge \left||x|-|z|\right|\\ ...
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3answers
40 views

Right angle triangle only area given

A right angle triangle has area 6 cm square. Is it possible to find the perimeter of the triangle?
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1answer
45 views

Law of Sines - Not Working?

Sorry that i cant post a picture (i dont have 10 rep), so this might be confusing. Basically i had a bunch of lines , two parallel, and 2 transversal lines going through them, making a triangle. The ...
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0answers
35 views

median of altered triangle [duplicate]

an equilateral triangle of 2 fixed sides N is given. how to check if it was possible to transform the triangle keeping two sides fixed and alter the third side such that it still remains a triangle, ...
0
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1answer
85 views

Area of convex n-gon using triangles

Suppose we have a convex $n$-gon and a point inside the $n$-gon or on the sides of the $n$-gon, and suppose one extended lines from all the vertices of the $n$-gon to make $n$ triangles with two of ...
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1answer
83 views

Proofs involving triangles and rectangles

The figure below represents a rectangle ACLK with an inscribed right triangle ABC. The lower case letters represent lengths of segments (ex. x=|KB|, etc. a.) prove that triangle ABC is similar to ...
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1answer
54 views

proof the triangle similarity

The figure below represents arbitrary triangle ABC. The points K,L,M are the midpoints of its sides. a) Show that triangle CLK ~ triangle CAB (and similarly for the other two corner triangles) How ...
0
votes
1answer
59 views

Pythagorean triplet .

You are given hypotenuse $h$ of triangle . Can you find out whether integral pythagorean triplet can be formed or not ? e.g given $h = 15$ . You can form triplet as $15,12,9$ because $15^2 = 12^2 + ...
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vote
2answers
962 views

Convert Equilateral triangle to Isosceles triangle

Let an equilateral triangle have the length of each side an integer $N$. I need to find if it is possible to transform the triangle keeping two sides fixed and alter the third side such that it still ...
1
vote
2answers
33 views

How to determine a point in a triangle in a high dimension?

I have 3 points: $(x1, x2, x3) \in R^d$ Given a query point $q \in R^d$, how can I efficiently determine whether $q$ resides inside the triangle that is defined by $(x1, x2, x3)$ ? Thanks!
1
vote
2answers
685 views

Given a number say $x$, How do you check if it can become hypotenuse of right angle triangle and other sides must be integers?

Given a number say $x$, how to check if it can become hypotenuse of right angle triangle and other sides must be integer For example: $5$ it can be hypotenuse as its other sides $3$ & $4$ are ...
0
votes
1answer
66 views

Finding the radius of the smallest circle that can circumscribe an equilateral triangle

Q:A puzzle board is in the form of an equilateral triangle that has an area of $7\sqrt{3}$ if the board is placed on a circular table, what should be the min area of the table so that the whole board ...