For questions about properties and applications of triangles

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1answer
271 views

Gergonne Point of a triangle coinciding with other triangle centers

I am trying to prove the following: Let $T$ be the Gergonne point (the intersection of the lines that connect the points of tangency of the incircle with the vertices of the triangle) of $\triangle ...
2
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1answer
81 views

Is there an exploitable relationship between the angles of AB and AC in a triangle when moving point A?

I'm writing software to dynamically create a random, generated world (civ-esque), populate it with settlements, and draw roads between them. It would be relatively easy to draw roads like this: ...
4
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2answers
162 views

Coordinates of parallel triangle with a distance of 'd' between the parallel edges?

I have a triangle with Co-ordinates $\{(x_1,y_1),(x_2,y_2),(x_3,y_3)\}$. I need to find co-ordinates of a triangle,whose edges are exactly $\alpha$ distance from previous triangle. Below is the figure ...
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4answers
224 views

Triangle proof using law of sines

In triangle $ABC$, suppose that angle $C$ is twice angle $A$. Use the law of sines to show that $ab= c^2 - a^2$.
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2answers
133 views

Minimizing the length of a pipeline between cities

I have been trying to minimize piping going to two different cities. City A is located at $(0,4)$ and city B is located at $(6,3)$. The cities must connect to the $x$-axis (the main pipe line.) It ...
1
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1answer
669 views

arithmetic progression of triangle sides

Let $gcd(a,b,c)=1$ such that $a^2, b^2, c^2$ are in arithmetic progression. Show they can be written in the form $a=-p^2+2pq+q^2$ $b=p^2+q^2$ $c=p^2+2pq-q^2$ for relatively prime integers $p,q$ of ...
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2answers
107 views

How to find co ordinates of a triangle after increasing the area by a factor of $\alpha$?

i am given with a triangle $\{(x_1,y_1),(x_2,y_2),(x_3,y_3)\}$ and the area need to be increased by a factor $\alpha$. can i anyone let me know formula to find the co ordinates of new triangle? There ...
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1answer
108 views

Triangle $z$-index interpolation between the vertices

I got a $2$D triangle, each vertex has a $2$D coordinate with a $z$-index value (NOT a $z$ coordinate!). The $z$-index value indicates whether a vertex lays on, in front of, or behind your screen ...
3
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1answer
325 views

Geometry - optimal 2D mesh between X expendable points

Say you have X points on a plane. If you connect two points, you form a line. Connecting three points forms a triangle. A line cannot cross a line, and a smaller triangle cannot be created inside a ...
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2answers
270 views

A question on Trigonometry (bisector)

If two bisector of a triangular is equal, then it is Isosceles triangular.
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2answers
156 views

Triangle $\Delta ABC$ , $a,b,c$ are in G.P.

If in a triangle $\Delta ABC$ the sides $a,b,c $ are in Geometric Progression.Find out the range of common ratio of the Geometric Progression. I understood that the twist is that we are bound under ...
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1answer
113 views

Law sines in Spherical Triangle $\rightarrow$ Law sines in plane triangle

Could any one tell me how to estimate or get law of sines in Spherical Triangle to The Law of Sines in Plane Triangle? i.e $\frac{\sin a}{\sin A}=\frac{sin b}{\sin B}=\frac{\sin c}{\sin C}$ to ...
2
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1answer
400 views

Finding side and angle of isosceles triangle inside two circles

I'm having a problem that I'm not sure how to solve (or if it's even possible). It's not homework, just something I'm struggling with for a project. :) Basically, there are two circles, represented ...
6
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2answers
143 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 ...
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1answer
108 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
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1answer
1k 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
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2answers
742 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
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4answers
402 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
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2answers
116 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
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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 ...
4
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1answer
136 views

Packing three squares into an equilateral triangle

I am trying to pack 3 equal, largest possible sized squares into an equilateral triangle.
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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?
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1answer
5k 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 ...
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1answer
297 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 ...
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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 ...
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2answers
481 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.
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2answers
65 views

Triangle that deals in terms of a and b?

What would be the correct way to approach this problem?
3
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1answer
592 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
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1answer
122 views

Geometric inequality with a triangle

The positive real numbers $x,y,z$ are the side lengths of a triangle iff $$x^2 + y^2 + z^2 < 2\sqrt{x^2y^2 + y^2z^2 + z^2x^2}$$
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1answer
339 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
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4answers
741 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
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3answers
3k 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 ...
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2answers
2k views

How do I find the base sides of this triangle?

In the figure above, what is the Value of PT/PS ?
2
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3answers
87 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
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3answers
180 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 ...
9
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2answers
13k 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 ...
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2answers
137 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?
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2answers
89 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
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1answer
102 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
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1answer
25k 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
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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
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0answers
104 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
3k 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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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
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2answers
165 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
696 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
203 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
39k 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
148 views

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

Any idea about this problem: As shown in the figure: Prove that $X=30.$