For questions about properties and applications of triangles

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1answer
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maths - find vertices when 1 vertex and center point is given in polygon

I want to know if there is any general formula to find out vertices (co-ordinates) of a polygon (3 or more equal sides) when following is given: ...
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4answers
444 views

What is so special about triangles?!

Take any random triangle. If we draw internal-angle-bisectors of all its angles, they intersect at the same point. If we draw the perpendicular bisectors of each side (although they aren't ...
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2answers
67 views

Proving a triangle equilateral given condition $al_a^2+bl_b^2+cl_c^2=9R\Delta$

$ABC$ is a triangle, with $l_a$, $l_b$, $l_c$ as angle bisectors, $R$ as circumradius and $\Delta$ as area, such that: $$al_a^2+bl_b^2+cl_c^2=9R\Delta$$ Is it true that $ABC$ is equilateral? I am ...
7
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2answers
577 views

Problem with the Pythagorean theorem [duplicate]

The Pythagorean theorem has already been proved and it is a basic fact of math. It always works, and there are proofs of it. But I have found a problem. Say you want to get from point ...
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4answers
142 views

Is there an integer that $\sqrt{3}$ can be multiplied by that will produce a whole integer?

The question came up while messing around with graph paper. I wanted to make an isosceles triangle where the length of one side and it's hight were both integers. The closest I could get was a base ...
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2answers
239 views

Does “triangle” in English exclude degenerate triangles?

Just for fun read few problems on the projeteuler.net website. Number 276 found interesting: Consider the triangles with integer sides a, b and c with a ≤ b ≤ c. An integer sided triangle ...
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2answers
436 views

Proving $\cot(A)\cot(B)+\cot(B)\cot(C)+\cot(C)\cot(A)=1$

I was stumped by another past-year question: In $\triangle ABC$, prove that $$\cot(A)\cot(B)+\cot(B)\cot(C)+\cot(C)\cot(A)=1.$$ Here's what I have done so far: I tried to replace $C$, using ...
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1answer
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Finding the distance between two gears

I have the following problem: In my class, we did a majorly complicated method to figure this out but I think there is a better way to do this... Here is the exact problem: A belt fits snugly ...
3
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3answers
76 views

Right-Angled Isosceles Triangle covering puzzle

Consider a RAIT (right-angled isosceles triangle), from which we remove a RAIT smaller than half its area by a cut perpendicular to the hypotenuse, like this: How many RAITs are required to cover ...
3
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2answers
914 views

How do you find the height of a triangle given $3$ angles and the base side? Image given.

This question has me absolutely stumped. This is the image of the question, how can I work out $x$? I've been doing a variety of attempts but I just cant get it.
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3answers
767 views

How many triangles can be created from a grid of certain dimensions?

How would you determine how many non-degenerate triangles can be drawn by connecting points in a $5 \times 5$ grid?
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1answer
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Given a particular triangle that has been constructed, I want to prove that one of the angles must be $> 45$ degrees. [duplicate]

Suppose you are given an acute triangle $XYZ$ with the following properties: At $\angle XZY$, the $\angle$ bisector is drawn and extended all the way to $XY$. Lets call the point where it intersects ...
2
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2answers
108 views

Equal perimeters of squares and right angled isosceles triangles

Consider a square ABCD having length l and breadth. Now start folding the sides AB and AC so that the figure becomes something like this $$$$ All the vertical and horizontal folds/stairs are equal in ...
2
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1answer
90 views

Distances to line passing through the centroid of triangle

Let $p$ be a line that pass through the centroid of a triangle $ABC$. Unless the line pass through one vertex, then $2$ verices are one side of the line, while the third one is on the other side. ...
2
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1answer
417 views

Calculate angle of triangle

I need to calculate the angle between two sides, I have the length of A & B sides, but don't know how to find the angle... Both sides are the same length. I can get the start and end vectors of ...
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 $A(cos(3-t),sin(3-t))$ $B(cos(t),sin(t))$ ...
2
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1answer
479 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. ...
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3answers
394 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
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2answers
8k views

Finding the area of triangle if length of medians are given

My question is: In triangle ABC ,length of median from vertex A is $13$ , length of median from vertex B is $14$ , length of median from vertex C is $15$. Compute the area of triangle ABC.
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1answer
35 views

What is the range of angle in front of longest triangle edge?

What is the minimum and the maximum values of the angle $\gamma$ in front of the longest triangle edge?
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4answers
142 views

Using the Law of Sines to find all triangles with given values of two sides and an angle

Our teacher skimmed over this and we have homework over it. Textbook is mostly unhelpful. I'm confused on how ambiguous case works, and everything I see online just confuses me more. I'm not quite ...
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1answer
270 views

equality of triangle inequality

$z$ and $w$ be nonzero complex numbers. How do I show that $|z+w|=|z|+|w|$ if and only if $z=sw$ for some real positive number $s$. I approached this by letting $z=a+ib$, and $w=c+id$, and kinda ...
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3answers
188 views

Prove that point M is on circle c

It's hard to create question names that make sense. Anyhow, the following is another question from my math assignment. Line-segment AB has a fixed length of 10 units. point A moves on the positive ...
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4answers
184 views

Inverse triangle equality [duplicate]

Possible Duplicate: Why exactly can you take the absolute value of one side of this inequality and assume it is still true? Why is $||a|-|b|| \ge |a|-|b|$, tried a lot (like comparing to ...
0
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1answer
33 views

who discovered the orthocenter of a triangle?

I tried to answer Is there a name for this result in planar geometry? and wanted to go back to the first mention of the orthocenter (or even the altitude of a triangle, but i did draw a complete ...
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2answers
55 views

No. of equilateral triangles required to completely fill a bigger equilateral triangle

$\triangle ABC$ is equilateral with side length=2.1cm Smaller equilateral triangles with side length=1cm are placed over $\triangle ABC$ so that it is fully covered. Find the minimum number of such ...
0
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1answer
30 views

Reverse triangle inequalities with three elements

Could you help me to show that $$ |a-b-c|\geq |b|-|a|-|c| $$ ?
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1answer
147 views

Prove vertex-orthocenter distance is twice of side_midpoint-circumcenter distance

$AL$ , $BM$ , $CN$ are altitudes , $TD$ , $RF$ , $ES$ are perpendicular bisectors of sides. How to prove $AQ = 2PD$ ? By similar triangles $\triangle AQN \sim \triangle CQL$ and $ \triangle CQL \sim ...
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1answer
959 views

Proof of ASA , SAS , RHS , SSS congruency theorem

I have tried searching in many places for some good proofs of these theorems but couldn't find them anywhere . Even my math teacher cannot explain it to me and says that these theorems just work. I ...
0
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1answer
1k views

Solving triangles and quadratic equations

When calculating the pieces in a triangle with only two sides and an intermediate angle is known, one must solve a quadratic equation. By solving the equation are 2, 1 or 0 solutions, as ...
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1answer
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How to prove we could use mass point geometry to solve all the triangle problem involving ratio between line segment and transversal in a triangle?

what is an easy way to prove that use mass point geometry to solve a problem in the link i provide that is involving cevians in a triangle is same as using the other way in euclidean geometry or ...