For questions about triangles

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2
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3answers
985 views

Proof of Cauchy–Schwarz inequality

I was reading about the Cauchy–Schwarz inequality from Courant, Hilbert - Methods Of Mathematical Physics Vol 1 and I can not understand what they mean when they said the line that has been ...
0
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0answers
97 views

Sum of angles in a hyperbolic triangle with one ideal angle

I want to calculate the sum of the angles of the triangle formed in the hyperbolic plane from the points $(-1,1), (0,1)$, and $(1,1)$. This forms an angle at the origin which has an infinite slope for ...
2
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1answer
2k views

Calculating circle radius from two points on circumference (for game movement)

I'm designing a game where objects have to move along a series of waypoints. The object has a speed and a maximum turn rate. When moving between points p1 and p2 it will move in a circular curve ...
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vote
1answer
2k views

How would I find the area of a triangle given three sides and using either the sine/cosine laws?

Triangle ABC has sides $8.5m$ (a), $7.1$ (b), and $9$ (c). I have been asked to find the area of the triangle using trigonometry.
2
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2answers
160 views

Solving for the length of a side of a triangle

I have a problem in which I'm supposed to solve for the length of the two sides of the triangle below. I assumed that it would simply boil down to $x+5=\sqrt{4x+52}$, and converted to standard form, ...
4
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2answers
565 views

Combinatorics. Inscribed Triangle in a decagon. No shared sides.

How many different triangles can be inscribed inside a regular decagon such that the triangle shares its vertices with the vertices of the decagon, but the triangle shares none of its sides? Here is ...
0
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1answer
45 views

10.5“ and 32” hypotenuse, a=8.5, b=42.5, what angles are the 10.5“ and 32” Hypotenuse?

I have a ramp that has a concave "kink" in the angle. The first length of the hypotenuse is 10.5", the next is 32". The triangle is 8.5" tall (a) The triangle is 42.5" long (b) How do I figure ...
3
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1answer
184 views

points inside square that form a triangle

the following question beat me. How from given any 9 points inside a square of side 1 we can always find 3 which form a triangle with area less than $1/8$ .
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4answers
31k views

Given the base and angles of an isosceles triangle, how to find length of the two sides?

I can't seem to find a textbook solution to this. It is always assumed that the length of the sides is know. Isolceles triangle So the base $a$ is known. The bottom angles where $\alpha$ and the ...
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2answers
146 views

As shown in the figure: Prove that $X=30.$

Any idea about this problem: As shown in the figure: Prove that $X=30.$
4
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2answers
1k views

Can every triangle be divided into five isosceles triangles?

That's my problem: Can every triangle be divided into five isosceles triangles? I've got to give evidence why this is true or not true... (sorry for possible language mistakes - I'm from Germany) ...
52
votes
10answers
9k views

What's a proof that the angles of a triangle add up to 180°?

Back in grade school, I had a solution involving "folding the triangle" into a rectangle half the area, and seeing that all the angles met at a point. However, now that I'm in university, I'm not ...
0
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2answers
496 views

3d geometry: triangle 2 points known, find 3rd point

I have a 3d triangle ABC. Lengths AB, BC, and AC are known. Coordinates of points A and B are known. Point C only the y value of the coordinate is known. I believe there are 2 points that can satisfy ...
3
votes
1answer
139 views

High School Geometry - If $BC$ is the greatest side of $\triangle ABC$, $D$ & $E$ are points on $BC, CA$…

If $BC$ is the greatest side of $\triangle ABC$, and $D$ & $E$ are points on $BC$ & $CA$, respectively, prove that $BC \ge DE$. Clearly, equality holds iff $D$ is on $B$ and $E$ is on ...
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3answers
172 views

How do I show that the pythagoras theorem holds for the specific case of an “isosceles right triangle”?

Figure shows a rectangle $ABCD$ and an isosceles triangle $\triangle DEC$. $AD=BC=z$;$AB=DC=y$;$DE=CE=x$ One solution is as follows. We know that the pythagoras theorem holds for a right triangle ...
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vote
1answer
2k views

Finding the line integral around a triangle

How can I determine $\int xy \;ds$ of a triangle with points $(0,0)$, $(1,0)$ and $(1,1)$ *The integral has the letter $C$, which I am not sure how to input here. I know it may seem easy, but I am ...
2
votes
4answers
627 views

How can every triangle have a circumcircle

Let's take for example $\triangle ABC$ with $\angle A = \angle B = 1^o$. How can a triangle like this have a circumcircle? My confusion is with triangles like this in general, with very long sides.
1
vote
3answers
209 views

Does every set of any three vertices of a cube determine a right triangle?

I recently came across this in my textbook: Any three vertices of a cube determine a right triangle. Is this a true statment? My initial thought was that is was, but the answers say otherwise. ...
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2answers
101 views

Calculating meeting point where line intersects arch

How do I find the point $p$ where the arch meets the red line if the angle of the blue are is known and the height of the yellow?
2
votes
4answers
703 views

Calculating an angle adjacent to hypotenuse given two points

I'm working on a chapter in my book dealing with touch input, and my memory of high school trig (from circa 1988) is failing me. My search here has not yielded anything that I'm capable of applying to ...
0
votes
3answers
75 views

Is this triangle possible to draw?

If the triangle must have the following sides: DE = 3cm DF = 8cm EF = 4cm And not taking into consideration anything about the angles. Is it possible to draw such a triangle?
0
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0answers
134 views

Determining a point in 3D space

So given a point, a rotation around the y-axis, a rotation around the x-axis, and a distance, how can one calculate the relative point in space? For example, the beginning coordinates are (0,0,0). ...
1
vote
1answer
145 views

Triangle inequalities, with angle bisector

I came across this question while I was taking one of the pratice Mu Alpha Theta tests for my school and I wasn't sure how to solve it. It reads: In $\Delta USA $, $\angle S$ is bisected by ...
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1answer
238 views

Squares in a triangle?

I've got some trouble... IJKL is a square and B, I, J, C are aligned (alternatively, |IJ| is confounded with |BC|. h is the height of acute $\triangle$ ABC from A to side BC. C1 is the red ...
0
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1answer
92 views

a triangle problem of angles

suppose in triangle ABC , angle of BAC is 60 degree. if K is intersection point of [CM] median(for segment[AB] )and [BN] altitude. also suppose |KM|=1 cm and |CK|=6 cm calculate angels of triangle ...
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2answers
924 views

Minimizing (and maximizing) the area of triangles

How would one solve questions like this one here in general? I have gotten an answer for that question, but I don't understand what's the intuition behind it. Can smoeone clearly explain how to ...
3
votes
4answers
2k views

Find an angle in a given triangle

$\triangle ABC$ has sides $AC = BC$ and $\angle ACB = 96^\circ$. $D$ is a point in $\triangle ABC$ such that $\angle DAB = 18^\circ$ and $\angle DBA = 30^\circ$. What is the measure (in degrees) of ...
3
votes
1answer
3k views

Compute the length of an equilateral triangle's side given the area?

Given the area of an equilateral triangle, what is an algorithm to determine the length of a side?
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0answers
35 views

Looking for different (analytical) approaches to a problem

Given 5 points in the plane any three of which are vertices of a triangle. Prove that among these triangles there is an obtuse triangle. I was able to prove it by examining all possible cases. I ...
5
votes
3answers
323 views

On Ceva's Theorem?

The famous Ceva's Theorem on a triangle $\Delta \text{ABC}$ $$\frac{AJ}{JB} \cdot \frac{BI}{IC} \cdot \frac{CK}{EK} = 1$$ is usually proven using the property that the area of a triangle of ...
2
votes
1answer
197 views

Altitude of tetrahedron?

I'm really curious to know any relationships between the altitude of a tetrahedron and how the foot of this altitude splits the base triangle. For example if you have a tetrahedron PABC with apex P, ...
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2answers
296 views

Triangle in hexagon

In a regular hexagon ABCDEF is the midpoint (G)of the sides FE and S intersection of lines AC and GB. (a) What is the relationship shared point of straight ...
3
votes
1answer
74 views

Solution for the value of angle $A$ of a triangle

In triangle $\triangle \; ABC$ , if $$2\frac{\cos A}{a} + \frac{\cos B}{b} + 2\frac{\cos C}{c} = \frac{a}{bc} + \frac{b}{ca}$$ find angle $A$. This is a quiz bee problem sent to me by my friend in ...
4
votes
2answers
482 views

Construct a triangle given one side, its height and inradius

I've been scratching my head with this problem: "Draw a triangle given one of its sides, the height of that side and the inradius." Now, I can calculate the area and obtain the semiperimeter. From ...
2
votes
4answers
1k views

what's the name of the theorem:median of right-triangle hypotenuse is always half of it

This question is related to one of my previous questions. The answer to that question included a theorem: "The median on the hypotenuse of a right triangle equals one-half the hypotenuse". When I ...
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3answers
160 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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vote
1answer
5k views

How to calculate radius when I know the tangent line length?

For my math homework, I was asked this question: The tangent lines from O hit a circle with center M and radius r in R and S. Calculate r. -The length of OR and OS is 4 How do I calculate the ...
2
votes
2answers
2k views

How do you find the equation for the angle bisecting line given three coordinates that make up an angle?

I have three points,$$A =[A_x,A_y]\,,\, B =[B_x,B_y]\,,\,C =[C_x,C_y]$$ How could one calculate the equation for the line that bisects the angle $\,\angle ABC\,$ (eg., passing through $B$)?
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2answers
1k views

Does the angle bisector always pass through the midpoint of any line segment between the two sides of the angle?

Consider this image: will the angle bisector of angle AOB always pass through the midpoint of AB, regardless of the lengths of AO and BO?
1
vote
3answers
79 views

Prove that altitude² = pq?

The following is a question for my math class. I just cannot figure it out. Given is that: h is the altitude that divides the longest side of this right triangle into p and q. Question: Prove that ...
1
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1answer
458 views

Integer solutions to linear equation – Triangle with set perimeter

We have a triangle with the sides a, b and c where: ...
3
votes
1answer
425 views

Area of triangle ABC inside circle

Consider the following diagram: $AB+AD=DE$, $\angle BAD= 60$, and $AE$ is $6$. How do we find the area of the triangle $ABC$?
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1answer
161 views

find distance from point in circle to perimiter

If I have the following circle, with centre in red and a random point in the circle in blue. I know the radius ,r, length of d, and the angle p: I then create a a new green point and I know the ...
3
votes
2answers
104 views

Triangle angles

How would I prove that, in any triangle, any of the exterior angles is bigger than any of the remote interior angles? Help would be much appreciated!
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0answers
35 views

How to prove this relationship between sides length in the specific triangle? [duplicate]

Possible Duplicate: Proving that $|CA|+|CB|=2|AB|$ in a general $ABC$ triangle When I was exploring a web collection with geometrical problems I found this one: How can I prove that in ...
0
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2answers
110 views

Angular radius of a sphere

Given a sphere with radius $r$ about a point $c$, what's the apparent angular radius $\alpha$ of that sphere from point $P$? In other words, if $\vec{o} = c - P$, what's the maximum angle another ...
3
votes
2answers
192 views

Geometry - Area of Siamese Triangles

How can I find the Area of this figure? It is quite curious because it is a particular case of this sequence: Anyone know how to find the area of this sequence as a function of the number of ...
3
votes
0answers
51 views

How many unique centroids? [duplicate]

Possible Duplicate: How many positions for centroid of triangle? Suppose that we are given 40 points equally spaced around the perimeter of a square, so that four of them are located at the ...
2
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2answers
167 views

Proving that $|CA|+|CB|=2|AB|$ in a general $ABC$ triangle

How in this situation (presented in image) can I prove that $|CA|+|CB|=2|AB|$?
0
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2answers
97 views

Difference between $\angle ABC = 90^o$ and $\angle B = 90^O$

When you have a random triangle $\triangle ABC$, what exactly is the difference between $\angle ABC = 90^o$ and $\angle B = 90^o$? In which cases is it the same, in which cases is it different? What ...