For questions about triangles

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2
votes
2answers
166 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
votes
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 ...
0
votes
3answers
83 views

Calculate incircle radius.

A circle is inscribed in a right angled triangle ABC where AC is the hypotenuse. The circle touches AC at point P. Length of AP = 2unit and CP = 4 units. What is the radius of the circle?
4
votes
4answers
751 views

Constructing a triangle given three concurrent cevians?

Well, I've been taught how to construct triangles given the $3$ sides, the $3$ angles and etc. This question came up and the first thing I wondered was if the three altitudes (medians, ...
2
votes
1answer
249 views

Prove that the Simson line of $P$ bisects the segment $HP$ from the orthocentre $H$ to $P$

Let $ABC$ be a triangle with orthocentre $H$ and circumcircle $\odot(ABC)$. Suppose $P\in\odot(ABC)$. Let $\gamma$ be Simson's line of $P$ wrt $ABC$. Prove that $\gamma$ bisects $PH$.
2
votes
1answer
144 views

Inequality in Triangles

Given is a triangle on points x,y,z in the plane. This triangle has two points a and b on different sides. I would like to show that the following inequality has to hold: $\max \{d(b,x), d(b,y), ...
1
vote
0answers
65 views

How to find the inverse position inside a triangle

If i were standing in a triangle - How do i calculate the inverse of my position? Can it be done? It's easy inside a rectangle, but I can't think of how you would do it inside of a triangle. I'm ...
2
votes
3answers
158 views

Sides of triangle and an altitude

Let $a$, $b$, $c$ be the lengths of the sides of a triangle. Let $h$ be the altitude drawn on the side of length $a$ Then is $a^2 + 4h^2 - (b+c)^2$ always negative ?
1
vote
1answer
127 views

Finding angles from some other angles related to incircle

Let $ABC$ be a triangle and $O$ the center of its enscribed circle. Let $M = BO \cap AC$ and $N=CO \cap AB$ such that $\measuredangle NMB = 30°, \measuredangle MNC = 50°$. Find $\angle ABC, \angle ...
1
vote
1answer
236 views

Barycentric coordinates of a triangle

I have to do what described in the picture below. Any ideas on how to do this?
2
votes
1answer
43 views

Trigonometric bounds

Is there a nice way to show: $\sin(x) + \sin(y) + \sin(z) \geq 2$ for all $x,y,z$ such that $0 \leq x,y,z \leq \frac{\pi}{2}$ and $x + y + z = \pi$?
-2
votes
3answers
2k views

Triangle inequality for subtraction?

Is the following inequality(that looks like the triangle inequality) valid: $|a - b| \leq |a| - |b|$ Why?
6
votes
2answers
154 views

A question on elementary plane geometry

Given a triangle $ABC$, let $S$ be an inner point of this triangle. Let $P$, $Q$, $R$ be the orthogonal projection of $S$ respectively on the three sides of this triangle. Are there beautiful methods ...
5
votes
3answers
451 views

geometry triangles side-side-side | prove my teacher she is wrong?

First time I'm here, I'M REALLY frustrated by now. So I'll just give u the question first. ...
3
votes
2answers
316 views

Similarity involving Miquel's Theorem

Let $\Delta ABC$ be a triangle. If we place points $D,\ E,\ F$ arbitrarily on the sides $\overline{AB},\ \overline{BC}$ and $\overline{CA}$ respectively, then the circumcircles of the triangles ...
0
votes
3answers
824 views

How to calculate radius of flush arch between two intersecting lines?

I am trying to make a corner of a robot I am designing flush for aesthetic reasons as well as safety reasons but I'm not sure how to make the arch of the corner lay flush with the two lines that make ...
0
votes
1answer
2k views

How many triangles can be formed from N points on a circle?

I have a circle with N points on it, and I want to determine how many triangles can be formed using these points. How can I do this? Thanks! Andrew
0
votes
1answer
31 views

Need help developing the formula to calculate the length of the y axis of a right triangle with a curved side for any position on the x axis.

If a right triangle has one side that is 500, another side that is 208, and the last side with a radius of 705, what is the formula to determine the length of the intersection point (y) at any given ...
0
votes
2answers
194 views

What is the logic to calculate triangle-inequality-theorem

So I want to know is there any simple formula to get the result for the triangle-inequality-theorem I know what is the theorem but any formula rather than doing it the routine way of adding then ...
1
vote
0answers
41 views

Triangular exponentation logarithm and inverse

The generalized formula of triangular exponentation on real numbers field is $x ^ {\triangle y} = \frac {1} {y \cdot B (x, y)} = \frac {\Gamma(x + y)} {\Gamma(x) \cdot \Gamma(y + 1)} $ It's my ...
2
votes
2answers
99 views

Generating integral triangles with two equal sides

How can I generate all triangles which have integral sides and area, and exactly two of its three sides are equal? For example, a triangle with sides ${5,5,6}$ satisfies these terms.
5
votes
7answers
8k views

Geometry triangle question

In the figure below, AB=BC=CD. If the area of triangle CDE is 42, what is the area of triangle ADG? I think triangles are similar. Are there any properties of similar triangles regarding their area. ...
3
votes
2answers
138 views

Showing that $ 1<\sin\frac{\alpha}{2}+\sin\frac{\beta}{2}+\sin\frac{\gamma}{2}$

I would like to show that: $$ 1<\sin\frac{\alpha}{2}+\sin\frac{\beta}{2}+\sin\frac{\gamma}{2}$$ where $\alpha, \beta, \gamma$ are the angles of a triangle. I know that the inequality $$ ...
4
votes
4answers
94 views

How is this angle relation true?

Either I'm silly and I'm missing something very simple, or my text book is incorrect. I'm trying to verify a line in the text book which claims that sin(a) = s/r. I can't seem to prove this to myself ...
0
votes
0answers
202 views

pixels in a projection of a triangle in 3d space onto a 3d plane through a pinhole camera

I have a triangle in 3d space. The x and y components of its vertices make a 2d right isoceles triangle. I am projecting it through a pinhole onto a plane. The projected triangles on the plane are now ...
6
votes
1answer
405 views

Geometry Proving Isosceles Triangle

This question seems tricky and I frankly don't know how to start. I will be grateful if someone can provide a solution. We have a triangle $ABC$ and there is a point $F$ on $BC$ such that $AF$ ...
0
votes
3answers
3k views

Calculate coordinates of 3rd point (vertex) of a scalene triangle if angles and sides are known.

I am writing a program and I need to calculate the 3rd point of a triangle if the other two points, all sides and angles are known. ...
1
vote
3answers
6k views

How to determine if a 3D triangle given by points is a right triangle?

How do I figure out if a triangle is a right triangle in 3-D space if you are given three points: $P = (3, -2, -3)$, $Q = (7, 0, 1)$, $R = (1, 2, 1)$? I know that it is an isosceles triangle (two ...
1
vote
2answers
296 views

2 Right triangles, which ratio is equal to 1?

Say you have a right triangle, you know the length of the 2 sides of the 90 degree corner (so you know everything, the hypotenuse and all 3 angles). Inside this triangle, you draw a line (not the ...
2
votes
1answer
1k views

How to calculate the rotation matrix between 2 3D triangles?

I need to calculate the rotation matrix and the translation vector between 2 given triangles in Euclidean space. This is really just a rotation and a translation, the lengths of sides of the triangle ...
2
votes
1answer
4k views

Trigonometry problem involving oblique triangle

How would I solve the following problem? A ship sails $15$ miles on a course $S40^\circ10'W$(south 40 degrees 10 minutes west) and then $21$ miles on a course $N28^\circ20'W$(north 28 degrees 20 ...
1
vote
2answers
706 views

What is the number of triangles with integer sides, given the length of the longest side?

Suppose $a,b,c \in\mathbb N$, and the value of $c$ is known and fixed, while $a$ and $b$ are unknown and are both smaller than $c$. What is the total number of unique triangles possible with $a, b$ ...
-2
votes
2answers
158 views

Consider a triangle with sides, $3,4,5$, does $3^2+4^2=5^2$ hold for such a triangle.

Consider a triangle with sides, $3,4,5$, let the angle opposite the greatest side $5$ be $\theta$, does $3^2+4^2=5^2$ hold for such a triangle. Now consider a triangle with sides (1,1,$\sqrt{2}$), let ...
3
votes
1answer
377 views

Is this a norm? (triangle inequality for weighted maximum norm)

I've been trying to prove that the following is a norm, but wasn't successful. I also cannot find a counterexample. So help is greatly appreciated. Let $x \in \mathbb{R}^N, \ w_i \in \mathbb{R}_+,\ ...
0
votes
1answer
100 views

how to find(measure,calculate) the distance (height,length) of an object?

I am trying to develope code ,so i need a mathematics help to proceed,please help me to find distance of an object using trigonometry r any applicable maths without using any sensors r external ...
8
votes
5answers
508 views

Maximum area of a triangle

I have been attempting to solve the problem here which is: Given three concentric circles of radii 1, 2, and 3, respectively, find the maximum area of a triangle that has one vertex on each of ...
1
vote
1answer
205 views

Scalar product equals weighted sum of projection of the vectors onto the edges of a simplex

Given a triangle with the edges $e_1$, $e_2$, $e_3$, it seems (from numerical evidence) that there are coefficients $\alpha_i$ such that $$ u^Hv = \sum_{i=1}^3 \alpha_i \, (u^He_i)\, (e_i^H v) $$ ...
0
votes
2answers
875 views

Will this problem be solved using Thales theorem for triangles

I am stumped on the following question: In triangle ABC , AD=DB , DE is parallel to BC. The area of Triangle ABC is 40. What is the area of triangle ADE I know Thales theorem must be ...
0
votes
1answer
75 views

Possibilities of x in a right angle tringle

I am stumped on the following question: Which of the following could be the value of x in the diagram a)10 b)20 c)30 d)40 e)50 (Ans b and c) Any suggestions relating to solving this ...
2
votes
2answers
439 views

Height of triangle inside a parallelogram

I am stumped on the following question PQRS is a parallelogram and ST=TR. What is the ratio of area of triangle QST to the area of parallelogram (Ans 1:4) I need the height of the ...
1
vote
2answers
454 views

Area of Triangle inside another Triangle

I am stumped on the following question: In the figure below $AD=4$ , $AB=3$ , and $CD=9$. What is the area of Triangle AEC? I need to solve this using trigonometric ratios however ...
2
votes
1answer
192 views

Trigonometric inequality for angles in triangle

Let $A, B, C$ be angles in a triangle. Is the following inequality $$4\cos A \le 1 + \cos\left(\frac{B-C}{2}\right)$$ true? I just assume it but don't have a proof. Thank you for your help.
0
votes
2answers
1k views

Deriving the formula for the radius of the circle inscribed in an equilateral triangle

I am trying to derive the formula for the radius of the circle inscribed in an equilateral triangle from scratch. Given $2*n$ = length of a side $H$ = the altitude of the triangle = $h + a$ ...
-1
votes
4answers
3k views

Perimeter of Triangle inside a circle

If the circle has a radius of 4, what is the perimeter of the inscribed equilateral triangle? Answer: $12\sqrt{3}$
0
votes
3answers
655 views

Triangle Inside Circle

If the radius of the circle is equal to the length of the chord $AB$, what is the value of $x$? How would I solve this problem ?
3
votes
1answer
202 views

How to find the area of green region in terms of yellow, blue and red region in the following figure?

How to find the area of green region in terms of yellow, blue and red region in the following figure? The triangle is any random triangle and an arbitrary point $P$ is taken where all the colored ...
6
votes
3answers
908 views

Why is the inradius of any triangle at most half its circumradius?

Is there any geometrically simple reason why the inradius of a triangle should be at most half its circumradius? I end up wanting the fact for this answer. I know of two proofs of this fact. Proof ...
4
votes
1answer
2k views

How many triangles with integral side lengths are possible, provided their perimeter is $36$ units?

How many triangles with integral side lengths are possible, provided their perimeter is $36$ units? My approach: Let the side lengths be $a, b, c$; now, $$a + b + c = 36$$ Now, $1 \leq a, b, c ...
0
votes
2answers
3k views

What is The 3rd side length of Isosceles Triangle

I've a isosceles triangle which length is $10\;\mathrm{cm}$ , $10\;\mathrm{cm}$ and $x$. If I want to make this triangle $120^\circ$ degree then what should be the $x$?