For questions about properties and applications of triangles

learn more… | top users | synonyms

2
votes
2answers
261 views

Finding the smallest possible angles in a triangle

I am having difficulty solving this problem: In the given figure (x+y) is an integer greater than 110. What is the smallest possible values of (w+z) (ans is 111)? Any suggestion on how ...
0
votes
1answer
336 views

Distributing points evenly between two fixed points

I have two fixed points, $P_1$ and $P_2$. I am trying to distribute $n$ points between them, so that the distance between every point is equal. This is easy when: distance between points $\cdot ...
4
votes
1answer
2k views

Whats the sum of the length of all the sides of a triangle?

You are given triangles with integer sides and one angle fixed at 120 degrees. If the length of the longest side is 28 and product of the remaining to sides is 240, what is the sum of all sides of the ...
2
votes
1answer
3k views

Maximum and Minimum Perimeter of a Triangle

I cant figure out the following question: A triangle has sides with lengths of 9,14 and h. if h is an integer what is the difference between the maximum and minimum possible perimeter of the ...
3
votes
1answer
689 views

Division into strictly isosceles acute triangles

What is the smallest number of strictly isosceles acute triangles that an equilateral triangle can be divided into? The following construction is by WR Somsky, with 13 triangles. Is this minimal?
1
vote
2answers
513 views

Calculating Perpendicular and Base of Triangle. Suggestion

In this diagram AB and CD are both perpendicular to BE.If EC=5 and CD=4. What is ratio of AB to BE ? How would i go about solving this triangle (without trigonometric ratios). I could ...
2
votes
2answers
516 views
1
vote
4answers
746 views

Perimeter of Triangle in a Right triangle.

I am having difficulty solving this problem: The perimeter of a right triangle is 18 inches. If the midpoints of three sides are joined by line segments they form another triangle . What is ...
1
vote
1answer
140 views

Calculating angles when sides are known - Without Trignometric ratios.

The question is: ABCD is a parallelogram and BFDE is a square . If AB is 20 and CF is 16 what is the perimeter of the parallelogram. The question is fairly simple and I know how to ...
0
votes
2answers
132 views

Which of the following cannot be the length of triangle

I have a question regarding triangles which is puzzling me: In triangle PQR , PR=7 and PQ=4.5 . Which of the following cannot represent the length of QR ? a)2.0 , b)3 , c)3.5 , d)4.5 , ...
1
vote
3answers
330 views

Finding Area of a Triangle without Trignometric ratios.

Hi I need to figure out the area of the following triangle, without using Trigonometric ratios. Any suggestions on the best approach. The answer is 12 square units Edit: I also think that the ...
2
votes
2answers
3k views

How to calculate coordinates of third point in a triangle (2D) knowing 2 points coordinates, all lenghts and all angles

I have a triangle and I know the coordinates of two vertices: $A=(x_1,y_1), B=(x_2,y_2)$ All the angles: $ABC = 90^\circ, CAB = 30^\circ$ and $BCA = 60^\circ$ and all the edge lengths. How can I find ...
9
votes
1answer
772 views

Is there a value for $\pi$ that relates to triangles?

So I heard that if one inscribes the largest circle that can fit into a equilateral triangle, then divides the perimeter of the triangle by the diameter of the inscribed circle, it gives a value which ...
2
votes
1answer
148 views

Length of the side of a discrete equilateral triangle from area

Firstly I haven't practised any mathematics in a long time, I understand that this might be pretty basic for math.stackexhcange, but I cannot seem to find any answers on the internet anywhere! I've ...
1
vote
1answer
107 views

How to graph this?

I have a non-right triangle. I will call the bottom or base edge $b$, the top left edge $a$, the top right edge $c$. Let $ a=c+2 $ and $b=10$. How do I graph a curve where the ...
2
votes
1answer
488 views

In center-excenter configuration in a right angled triangle

My question is: Given triangle ABC , where angle C=90 degrees. Prove that the set { s , s-a , s-b , s-c } is identical to { r , r1 , r2 , r3 }. *s=semiperimeter , r1,r2,r3 are the ex-radii. Any ...
3
votes
2answers
281 views

Angles of triangle inside a cricle

In the figure shown if area of circle with center o is 100pi and CA has length of 6 what is length of AB ? I looked around on the web and cant seem to get an idea of what the angles AOC ...
2
votes
1answer
148 views

Area of Square - Comparing squares

The question is: If the area of a parallelogram $JKLM$ is $n$ and if length of $KN$ is $n+(1/n)$, then find the length of $JM$. (The answer is $n^2 /( n^2+1 )$.) How would i go about ...
0
votes
2answers
2k views

Triangles inside a square

I have a question with a figure of Triangle inside a square. The base of the triangle is on the base of the square and the peak of the triangle touches the top of the square.It then asks the ratio ...
1
vote
1answer
224 views

Triangle related question 2

In triangle $\triangle ABC$, if $AD$ is the angle bisector of angle $\angle A$ then prove that $BD=\frac{BC \times AB}{AC + AB}$. Any help/hints to solve this problem would be greatly appreciated.
3
votes
1answer
2k views

Find length of segment in triangle

In triangle $ \bigtriangleup ABC$, the known sides are: $AB=5$, $BC=6$ and $AC=7$. A circle passes through points $A$ and $C$, crosses straight lines $BA$ and $BC$ at points $K$ and $L$, which is ...
0
votes
3answers
441 views

Solving problem: Area of Triangle

I have this data: $a=6$ $b=3\sqrt2 -\sqrt6$ $\alpha = 120°$ How to calculate the area of this triangle? there is picture:
2
votes
2answers
208 views

Triangle related question

My question is: In Triangle ABC , let AE be the angle bisector of angle A. If 1/AE = 1/AC + 1/AB , then prove that angle A = 120 degrees. What i tried: I extended side AB and took a point M on it ...
2
votes
3answers
181 views

Perimeter of a triangle

A question states: The length of each side of a certain triangle is an even number.If no two sides have the same length what is the smallest perimeter the triangle could have ? ...
1
vote
1answer
622 views

3D intersection point between circle and triangle

Given a 3D triangle with vertices $(v0, v1, v2)$ and a 3D circle of radius $r$, centered at $c$, and lying in the plane perpendicular to $axis$, how can I test for intersection points between them? ...
2
votes
0answers
111 views

triangles in a grid of $n\times n$ with positive coordinates

I need to count the number of triangles formed in a grid of $n\times n$ with positive integer coordinates $(0..n)$. For example for $n = 1$ the answer is 4.
1
vote
1answer
270 views

Marden’s Theorem

Given a triangle and three vertices in x, y format, is there a systematic way to use Marden’s Theorem to get the vertices of the foci of the inscribed ellipse? It seems to involve the derivative but ...
1
vote
1answer
562 views

triangle related challenge

In triangle $ABC$, $BA=BC$ and $\angle B=90^\circ$. $D,E$ are the points on $AB,BC$ respectively such that $AD=CE$. $M,N$ are points on $AC$ such that $DM$ is perpendicular to $AE$ and $BN$ is ...
-2
votes
4answers
570 views

Why are there isosceles triangles? [closed]

Why are isosceles triangles called that — or called anything? Why is their class given a name? Why did they find their way into the Elements and every single elementary geometry text and course ...
1
vote
1answer
516 views

Find point given a line and two angles

Let's say I have two points $p_1=(x_1, y_1)$ and $p_2=(x_2, y_2)$, which are given as two points of a triangle $T$. And let's say I know the angles of $T$ at $p_1$ and $p_2$. How do I find the third ...
2
votes
0answers
375 views

Euler's Line of a medial triangle

I have the following problem with a comment below on the steps that I took so far. Here is the example: Let triangle ABC be any triangle. The midpoints of the sides in Triangle ABC are labeled $A', ...
2
votes
2answers
472 views

Prove there exists a triangle without using Euclidean Parallel Postulate

Let $a$ and $b$ be real numbers where $0 < a< b<180$. Let $A$, $B$, $D$ be points so $A$-$B$-$D$. Part 1: Prove there exists a triangle $ABC$ where measure of angle $CAB$ is $a$ and measure ...
0
votes
1answer
30 views

a question on “basic triangle at q”

Could someonehelp me to understand these sentences: A “basic triangle at $q$” will mean a triangle which has the sides adjacent to the vertex $q$ of equal length and an angle at $q$ of measure ...
1
vote
1answer
718 views

Finding a point of an isosceles triangle *OR* Find the coordinates of the start-point of an angled line

How do I find the coordinates ?/? (green star) given n, A (angle) and ...
0
votes
1answer
2k views

Calculate new graph point with coordinate and angle

On a Cartesian graph I have a point at x = 0 and y = 0. This point needs to move forward at a 30 degree angle. It should travel forward at this angle for 1.75 on the graph. What equation can I use to ...
1
vote
3answers
653 views

angle of an inscribed triangle

I have a scalene triangle inscribed in a circle, one of its sides $a$ is $2\sqrt3$ and the length $r$ from that side to the center is $1$. I need to find the angle $x$ opposite to the side given. ...
3
votes
2answers
190 views

Stuck on geometry proving

Points S and D are respectively the center of the circle circumscribed on the acute triangle ABC and the orthocenter of this triangle. Prove that ASBX, where X is the center of the circle ...
1
vote
2answers
524 views

Find the radius of the circle?

Three circles of equal radii have been drawn inside an equilateral triangle , of side a , such that each circle touches the other two circles as well as two sides of triangle. Then find the radius ...
2
votes
2answers
2k views

The sides of an isosceles triangle from the circumradius and inradius

I need to solve the following problem only by using Pythagoras Theorem and congruent triangles. Find the sides of an isosceles triangle ABC with circumradius R=25 and inradius r=12.
4
votes
4answers
7k views

two sides and angle between them triangle question.

is it possible to find the third side of a triangle if you know the lengths of the other two and the angle between the known sides? the triangle is not equilateral. we're using the kinect camera and ...
3
votes
1answer
4k views

How does this equation to find the radius from 3 points actually work?

I had searched online and found an equation that solves the radius of a circle from 3 points that are located on the circumference of that specific circle. Where I had found this formula did not state ...
2
votes
3answers
655 views

Counting right triangles with integral hypotenuse and given integral height

Let h = the height of the right triangle (an integer). Let c = the hypotenuse Let l = the other leg So l^2+h^2=c^2 I am trying to figure out, for instance, why ...
11
votes
3answers
2k views

how to prove DEF is an equilateral triangle?

ABC is an equilateral triangle,and AD = BE = CF,Prove DEF is an equilateral triangle.
0
votes
2answers
46 views

Inner product in $\mathbb{R}^2$ and angles of a triangle

Let $P_1,P_2,P_3$ be $3$ different points in $\mathbb{R}$, then $P_1,P_2,P_3$ form a triangle. What is the relation between the (one of the) angles of this triangle and $\langle P_2-P_1,P_3-P_1 ...
0
votes
0answers
160 views

Get value of angle with 45 degrees as maximum and 0 and 90 degrees as minimum

I want the calculate the "value" of an angle in such a way that: The angle of 45 degrees corresponds with the maximum value of 1 The angles of 0 and 90 degrees correspond with the minimum value of 0 ...
0
votes
1answer
84 views

Algorithm for a geometry-problem

In a system I'm building I'd like to have a "point" that hangs from two wires. The length of these wires is variable. So basically I would have a triangle, two sides of which are "varible". Could ...
5
votes
3answers
21k views

how to calculate area of 3D triangle?

I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. ...
1
vote
2answers
218 views

Find the ratio in which the circle divides each of the sides AB and AC?

A circle passes through the vertex A of an equilateral triangle ABC and is tangent to BC at its midpoint . Find the ratio in which the circle divides each of the sides AB and AC? Does the line ...
1
vote
2answers
3k views

circle inscribed into isosceles triangle

i am trying to solve following problem: suppose that legs AB=BC=30 in isosceles triangle,and center of inscribed circle divides altitude into 12:5 part,our aim is to find base,my problem is that i ...
2
votes
2answers
216 views

rational triangles and cosines

I've recently started to try working on exercises from this book on Diophantine equations before I need to return it to the library. This one has me slightly stumped. It asks to show that the cosine ...