For questions about properties and applications of triangles

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6
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2answers
138 views

Concurrency of A'L, B'M, C'N.

Need some help with the following problem. Problem: In $\triangle ABC$ the midpoints of $BC$, $AC$, $AB$ are $L, M,$ and $N$ respectively, and the points on the circumcircle opposite to $A, B,$ and ...
1
vote
1answer
107 views

How to prove triangle inequality for given formula?

How to prove that given formula $\frac{(P-Q)^2}{P}+\frac{(P-Q)^2}{Q}$ satisfies triangle inequality ?
2
votes
1answer
654 views

Does the orthocenter have any special properties?

Each of the commonly known triangle centers I know has some sort of special property. For example: The incenter is the center of the inscribed circle. The circumcenter is the center of the circle ...
6
votes
2answers
660 views

Equilateral triangle geometric problem

I have an Equilateral triangle with unknown side $a$. The next thing I do is to make a random point inside the triangle $P$. The distance $|AP|=3$ cm, $|BP|=4$ cm, $|CP|=5$ cm. It is the red ...
2
votes
4answers
348 views

Circle/Triangle math problem

The question asks to find angles $\angle X$ and $\angle Y$, however I don't know how to do this without assuming that lines $\overline {GO}$ and $\overline{OJ}$ are parallel. The only angle given is ...
3
votes
2answers
109 views

Solving for the triangle's perimeter

Would like some help with solving for the grey triangle's perimeter. It is assumed that the grey triangle is equilateral. My attempt: Let $x =$ side of grey triangle Let $h =$ height of grey ...
7
votes
2answers
494 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 ...
4
votes
1answer
131 views

Packing three squares into an equilateral triangle

I am trying to pack 3 equal, largest possible sized squares into an equilateral triangle.
1
vote
0answers
35 views

Two coloured plane

Can you prove that For any two angles $θ,ϕ$ there exists a monochromatic triangle that has angles $θ,ϕ,180−(θ+ϕ)$ in two coloured plane?
0
votes
1answer
4k views

Determine angles of triangle given nothing (no scientific calculator) but triangle sides.

The question says it all. Given a triangle, find its angles without a calculator. Is this even possible without tables or making tables? Summary: Is it possible to determine the inverse sin, cos of ...
1
vote
1answer
270 views

Existence of Gergonne point, without Ceva theorem

The intersection at one point (called Gergonne point) of the lines from vertices of a triangle to contact points of the inscribed circle can be proved immediately using Ceva's theorem. Is there a ...
1
vote
3answers
2k views

Connecting midpoints of sides of a triangle

In triangle $\triangle ABC$, $AB=8$, $BC=14$ and $CA=10$. Points $M$, $N$, and $P $ are the midpoints of sides $AB$, $BC$, and $CA$, respectively. If $M$, $N$, and $P$ are connected to form a ...
1
vote
2answers
449 views

Finding the area of a triangle using fractions?

To find the area of the triangle do you use Pythagorean theorem from what you have? Could this use similar triangles.
0
votes
2answers
63 views

Triangle that deals in terms of a and b?

What would be the correct way to approach this problem?
3
votes
1answer
532 views

Construct a Triangle from Given Base, Obtuse Angle Adjacent to Base and Difference of Two Other Sides

I need to construct a triangle from given base, obtuse angle adjacent to base and difference of two other sides. Let us try to analyze the scenario. We are given base BC, obtuse ...
9
votes
1answer
118 views

Geometric inequality with a triangle

The positive real numbers $x,y,z$ are the side lengths of a triangle iff $$x^2 + y^2 + z^2 < 2\sqrt{x^2y^2 + y^2z^2 + z^2x^2}$$
0
votes
1answer
275 views

How to determine a Triangle vertices by its coordinates?

I have to solve this problem, yet I'm not sure what is asked. Given a triangle whose vertices are defined by its coordinates. Determine where is the point O with the given coordinates - inside or ...
6
votes
4answers
698 views

How to know location of a point?

I have a circle formed with three given points. How can i know whether another given point is inside the circle formed by previous three points. Is it determinant i need to calculate? Then what are ...
0
votes
3answers
2k views

Isosceles Triangle how to find the base?

Two sides of a triangle each have length of 5. All of the following could be the length of the third side Except. A 1 B 3 C 4 D 7.07 or √50 E 10 Do I use the formula 2√L^2-A^2 in order to find ...
3
votes
2answers
1k views

How do I find the base sides of this triangle?

In the figure above, what is the Value of PT/PS ?
2
votes
3answers
86 views

getting the inner corner angle

I have four points that make concave quad: now I wanna get the inner angle of the (b) corner in degrees. note: the inner angle is greater than 180 degree.
6
votes
3answers
160 views

What characteristic of the triangle leads the the existence of the orthocenter

We all know that all three altitudes of a triangle meets in the orthocenter of the triangle. It's a quite classical problem and is proven. However, what I really wanna know is what characteristic of ...
8
votes
2answers
10k views

How to find surface normal of a triangle

If I have a triangle with $3$ points $P_1, P_2,$ and $P_3$, each with $x, y,$ and $z$ coordinates, how do I find the surface normal $N$ in $x, y,$ and $z$ such that $$N_x+N_y+N_z = 1$$ I'm looking ...
1
vote
2answers
129 views

Question about Geometry involving angles and lines

The answer is C however if angle ACD is 110 degrees and angle AB is 110 degrees how does it equal 180?
1
vote
2answers
88 views

Help with basic trigonometry

it's been many years since I was at school and I never did algebra so I'm having a real hard time understanding trigonometry again. ALL the sites just say use this easy formula to calculate it: ...
3
votes
1answer
99 views

Why does $b^2 = c^2 + a^2 - 2ca\cos(B)$ in trigonometry?

http://i.stack.imgur.com/l0Dw7.png I have a (what I believe to be an isosceles) triangle and the formula $b^2 = c^2 + a^2 - 2ca \cos(B)$ and I just have to "prove it". Now this really confused me as ...
2
votes
1answer
21k views

How do I find the angles of a triangle if I only have the lengths of the sides?

Is it possible to find the angles of a triangle if I only have its sides? If so, how can I achieve this? Regarding my knowledge of triangles: Whilst I was taught trigonometry a few years ago, I ...
2
votes
3answers
1k 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
votes
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
votes
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 ...
1
vote
1answer
3k 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
votes
2answers
163 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
votes
2answers
599 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
votes
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
votes
1answer
188 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 $1/8$ .
2
votes
4answers
33k 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 ...
-4
votes
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
votes
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
votes
2answers
508 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 ...
-4
votes
3answers
174 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 ...
1
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
640 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
217 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. ...
0
votes
2answers
103 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
721 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
votes
0answers
136 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
148 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 ...