For questions about properties and applications of triangles

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2
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2answers
27 views

Find the area of the triangle under certain preconditions

With vertices $(0, 0)$, $(b, a)$, $(x, y)$, prove the area of this triangle is $\frac{|by - ax|}{2}$. We know area of a triangle = $\frac{rh}{2}$. ($r$ is the base.) Well, we have $r =$ the ...
0
votes
2answers
11k views

Length of hypotenuse using one side length and angle

I bet this question has been asked a million times, but I can't find a straight answer. I need to find the length of the hypotenuse in a triangle where I have one side and all the angles. Example: ...
0
votes
1answer
13 views

Finding third vertexes of any triangle where 2 vertex known and all sides length known

I am working with a CAD engine in the head but i working on code only. I have a rectangular tube that need to be put at an angle. I so have the diagonal of the tube where it has to start and stop but ...
2
votes
1answer
62 views

Calculationg the angle of a triangle

I am trying to find a specified angle of a triangle. In triangle $ABC$, $\angle A = 20^\circ$. $D$ and $E$ are points on $AB$ and $AC$, where $AB=AC$. $\angle EBC = 50^\circ$ and $\angle DCB = ...
5
votes
3answers
439 views

Prime Number in triangle

I had a question here, the measures of the sides of a right triangle (a single unit) can be prime numbers? If they can not, why?! But, if you can, could you help me find an example?
0
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0answers
41 views

Find the angle in a triangle [duplicate]

Find the angle $a$: I came up with 20 degrees but not sure. Can somebody help here.
0
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1answer
33 views

Relationships in a triangle

Here is the question, I can''t figure out how to explain this algebraically.
2
votes
1answer
61 views

Prove that the intersection of $BM$ and $CN$ is on the circumcircle of triangle $ABC.$

Let $P$ and $Q$ be on segment $BC$ of an acute triangle $ABC$ such that $\angle PAB$ = $\angle BCA$ and $\angle CAQ = \angle ABC$.Let $M$ and $N$ be the points on $AP$ and $AQ$, respectively, such ...
-3
votes
0answers
74 views

Do you have any idea?

Let $M$ be a point moving inside a triangle $ABC$ with all sharp angles, with the property that $$\angle(B) + \angle(AMC) = 180.$$ Knowing that $\{E\}:= AM \cap BC$ and that $\{F\}:=CM \cap BA$, ...
-1
votes
0answers
46 views

Find the lengths of two segments in a triangle with a line parallel to a side

Take a look at the picture, I am suppose to find the value of x and y. I have already manages to figure it out but here are a few questions that I need to understand. AD/AB = CE/CB = CA/ED x= ...
5
votes
1answer
101 views

Inequalites of triangle side with $abc = 1$

Let $a,b,c$ be the sides of a triangle with $abc=1$. Prove that $$ \frac{\sqrt{b+c−a}}{a} + \frac{\sqrt{c+a-b}}{b} + \frac{\sqrt{a+b−c}}{c} \ge a+b+c $$
0
votes
1answer
26 views

Z coordinates of 3rd point (vertex) of a right triangle given all data in 3D

this is my first post.. I hope this good I have 1 triangle in space (3D)... and I know all data except the coordinates of 3er point(vertex)... for example this: then: ...
-1
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0answers
8 views

find the perimeter of the quadrilateral [closed]

Given, perimeter of triangle QST IS 7+ROOT 13. Find the perimeter of PRST?
0
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2answers
448 views

How long is the shadow of a 6-foot tree planted 15 feet from a 18-foot lamp post? [closed]

A 6-foot spruce tree is planted 15 feet from a lighted streetlight whose lamp is 18 feet above the ground. How long is the shadow of that tree? My idea for finding the length of the shadow is ...
-4
votes
1answer
29 views

Which is true: $|x| - |y| < |x-y|$ OR $|x-y| < |x| - |y|$ [closed]

Which is true: (for rational numbers) $$ \lvert x \rvert - \lvert y \rvert < \lvert x - y \rvert $$ or $$ \lvert x-y \rvert < \lvert x \rvert - \lvert y \rvert $$ ? thanks in advance
0
votes
1answer
28 views

Find α (Triangles) [closed]

Find $\alpha$ if $A = 4\alpha$. Can someone explain to me how to do this?
2
votes
2answers
84 views

Geometry question about centroid

How do you solve this geometry question? In triangle $ABC$ the centroid is $G$ and $D$ is themidpoint of $CA$. The line through $G$ parallel to $BC$ meets $AB$ at $E$. Prove that $\angle ...
1
vote
0answers
22 views

Intersections of convex hulls

Given a set of $n$ points $\{A_1, \ldots , A_n\}$ of the plane and every possible triangle formed with $3$ points $A$, I would like to describe the intersections fo theses triangles. By intersection, ...
0
votes
1answer
17 views

Triangle Area Ratio Theorem Problems?

Having a hell of a lot of issues with these problems, supposed to be on the topic of triangle area ratio theorem (ratio area of triangles = ratio of triangles' heights x ratio of triangles' bases.) ...
1
vote
1answer
48 views

Proof of a set of triangles and unit squares

Suppose that there is $S$, a finite set of unit squares. So, $S$ is chosen from a larger grid of unit squares. The unit squares of $S$ are tiled with isoceles right triangles. Each of these triangles ...
1
vote
1answer
52 views

Proving $B$, $C$, $D'$ and $E'$ to be concyclic iff $AB+AC=3BC$?

Let $ABC$ be a triangle with incenter $I$. The incircle of $ABC$ touches $AC$ at $D$ and $AB$ at $E$. Let $DD'$ and $EE'$ be the diameters of the incircle. Prove that $B$, $C$, $D'$ and $E'$ are ...
1
vote
3answers
38 views

Proving that $BI$, $AE$ and $CF$ are concurrent?

Let $ABC$ be a triangle, and $BD$ be the angle bisector of $\angle B$. Let $DF$ and $DE$ be altitudes of $\triangle ADB$ and $\triangle CDB$ respectively, and $BI$ is an altitude of $\triangle ...
0
votes
1answer
30 views

How prove that $AB>AC$ in triangle $ABC$?

Point $D$ is chosen inside $\triangle ABC$, and point $E$ on segment $BD$ such that $BD=CE$. Suppose $\angle ABD=\angle ECD=10^{\circ}$, $\angle BAD=40^{\circ}$, and $\angle CED=60^{\circ}$.How prove ...
2
votes
1answer
18 views

Triangle Inequality with Vectors

If the magnitudes of vectors $\mathbf{a}$ and $\mathbf{b}$ are $5$ and $12$, respectively, then the magnitude of vector $(\mathbf{b-a})$ could NOT be (A) 5 (B) 7 (C) 10 (D) 12 (E) 17 The triangle ...
0
votes
0answers
38 views

Triangle $ABC$ and equilateral triangles $ABC'$, $BCA'$ and $ACB'$.

We consider a triangle $ABC$ whose angles are less then $120°$ and construct the equilateral triangles $ABC'$, $BCA'$ and $ACB'$, exterior to $ABC$. $I$ denotes the intersection of $(AA')$ and ...
2
votes
3answers
47 views

Given an equilateral triangle, show that $MA + MC = MB$.

I have to solve the following problem: Consider an equilateral triangle $ABC$ and $\mathcal{C}$ its circumscribed circle. Let $M$ be a point located on the arc of the circle defined by $[AC]$ which ...
0
votes
1answer
38 views

Triangle Identity leads to another Euclidean parallel.

Referring to TriangleIdentity by 伍柒貳 a while ago, considering $\bigtriangleup$ ABC, it is proved that: $$\sin^2A \equiv \cos^2B + \cos^2C + 2 \cos A\cos B\cos C (1*) $$ I want to take angle $A = ...
0
votes
0answers
22 views

Are isosceles right triangles the only ones whose circumcenters lie on their incircles? [duplicate]

I recently (stupidly) asked this question, to which user Blue responded quickly with the example of the isosceles right triangle. Which triangles have circumcenters on their incenters? Do they have to ...
1
vote
1answer
619 views

How to find coordinates of 3rd vertex of a right angles triangle when everything else is known?

I want to locate precisely the 3rd coordinate of a right angled triangle. I have: the length of three sides The three angles The other two coordinates of the triangle The triangle can lie in any ...
5
votes
3answers
22k 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
1answer
24 views

How many points $P$ such that $\angle APB=\angle BPC=\angle CPA $ are there?

Given that $\triangle ABC$ is arbitrary. How many points $P$ such that $\angle APB=\angle BPC=\angle CPA $ are there?
1
vote
4answers
48 views

Proving $\sin^2A \equiv \cos^2B + \cos^2C + 2 \cos A\cos B\cos C$

As the title, By considering $\bigtriangleup$ABC, Prove $$\sin^2A \equiv \cos^2B + \cos^2C + 2 \cos A\cos B\cos C$$ Thanks
0
votes
1answer
16 views

How to find heading angle to an object who's x,y coordinates are known?

Scenario: I have a map with a marked location on it. I know my x,y coordinates on the map (top left corner is 0,0), my distance from that marked location, my heading angle relative to true north (0 is ...
10
votes
1answer
93 views

Is there a name for the recursive incenter of the contact triangle?

Recently, I became aware that there are many more triangle centers than the four I learned about in school. This reminded me of a thought I had when I first learned about the incenter: what point ...
3
votes
0answers
57 views

Proving that $AB = AC$. [closed]

In a $\triangle ABC$, $D$ is a point on $BC$ such that $AB+BD=AC+CD$.Let the centroids of $\triangle$s $ABD$ and $ACD$, vertices $B$ and $C$ lie on a circle.Prove that $AB = AC$.
2
votes
3answers
77 views

Coordinate of the excentre of a triangle

I am just wondering that how the coordinate of the excentre comes out if we know the coordinates of vertices of the triangle.
1
vote
1answer
22 views

Find point in right triangle with given one vector and one point

I am developing a game where the user move a car with his finger. The car is represented as vector (one point and angle of rotation in the screen). When the user start to dragging the car he generate ...
2
votes
2answers
73 views

Prove that $\cos(2a) + \cos(2b) + \cos(2c) \geq -\frac{3}{2}$ for angles of a triangle

Let the three internal angles of a triangle are $a,b,c$. Prove that $$\cos(2a) + \cos(2b) + \cos(2c) \geq -\frac{3}{2}.$$ I'm looking for an elementary, geometric proof. So avoid derivatives and ...
3
votes
1answer
331 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 ...
2
votes
1answer
399 views

Triangle question

I am not able to solve this question from chapter "Similar & Congruent Triangles" in my book. Can some one help to calculate AC? .
2
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3answers
62 views

Proving $HH', BB', CC'$ are concurrent?

The orthocenter of $\triangle ABC$ is $H$. Let $B'$ be a point on AB and $C'$ be a point on AB, such that $BCB'C'$ is a cyclic quadrilateral. Let the orthocenter of $\triangle AB'C'$ be $H'$. ...
0
votes
0answers
15 views

General formula for n-Simplex side-lenghts given n-volume and angles

Given a flat triangle's three angles $\phi_i $, and its area $A$, you can calculate the $i$th sidelenght $s_i$ (using Einstein's sum-convention) like so: $$ s_i=\frac{\sqrt{2A} \sin \left(\phi ...
0
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0answers
20 views

ABC is a triangle, D is a point in the triangle. E is the midpoint of BD. AB=BC, angle ABD= angle DBC=35 degrees, angle ACD=25 degrees. Angle BAE=?

I tried to solve this problem but couldn't. I just know that here, angle BDC= 100 degrees, angle BAC= 40 degrees, AB^2+AD^2=2(AE^2+BE^2) and AB/AD={sin(angle DAE)}/{sin(angle BAE)}
1
vote
1answer
71 views

Root of sum of squared distances

Say I want to calculate the euclidean distance of all edges of a triangle. I could take the root of the squared distance of each edge and add those. This would give me the right result. Adding up ...
1
vote
0answers
16 views

Finding other two vertices when one vertex and each point on the triangle is known ?

I am working on some gesture recognition for my game. I am stuck on a problem. I have one vertex i.e the starting point and every point on the triangle, I also have the centroid. So how do I find the ...
0
votes
1answer
696 views

Determine if projection of 3D point onto plane is within a triangle

In 3D, given three points $P_1$, $P_2$, and $P_3$ spanning a non-degenerate triangle $T$. How to determine if the projection of a point $P$ onto the plane of $T$ lies within $T$?
0
votes
1answer
16 views

Finding other two vertices of a triangle from centroid and one vertex?

I am working on some gesture recognition for my game and I want to find if a point is inside the triangle created by the user or not. For that I need three vertices. Currently I am using the '$1 ...
2
votes
1answer
39 views

Minimum Distance between a Triangle and a Distance Field 3D

I am looking for (possibly numerical) solution to this geometric problem: Given a filled 3D triangle $T = \text{conv}(p_1, p_2, p_3) \subseteq R^3$, and a distance field $D(x) : R^3 \to R$, what ...
1
vote
1answer
45 views

Find closest point in triangle given barycentric coordinates outside

Given a non-degenerate triangle ABC and an arbitrary point P in 3D space, I can project P onto the plane defined by ABC and check whether the triangle contains it as described here. I end up with ...
3
votes
1answer
41 views

Closest point on a 3D triangle, is this algorithm correct?

Given a point $P$ and three triangle vertices $U$, $V$, $W$, all in $\mathbb{R}^3$, I need to find the point in the triangle $UVW$closest to $P$. Does the following algorithm work, or have I missed ...