For questions about triangles

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Finding angles in Barycentric system

How to find the angles of a triangle given the barycentric coordinates of its corners? Does it work if i take the first two components of every coordinate, and find the angles in the triangle (on the ...
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2answers
25 views

Find the value of EF and AC.

In the figure given below, BA, FE and CD are parallel lines. Given that AB = 15 cm, EG = 5 cm, GC = 10 cm and DC = 18 cm. Calculate EF and AC. I think the answer is EF= 8.66 and AC = 25.66 but I ...
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Generate X, Y, Z coordinates of 3D triangular prism with Edge Rounding

I'm trying to create an interactive 3D visualization with Python and Mayavi for inputs to an analysis program. The program accepts certain primitive shapes which it combines (constructive solid ...
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17 views

Solving for and x,y,z coordinate in a 3D plane

This is hard for me to explain, but basically I am making a game and I want a 3rd person like camera. I have a lot of information about how the camera should be but I can't seem to get the camera to ...
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Prove that two triangles are congruent

${ABC}$ and $A'B'C'$ are two triangles. Let $P$ be the midpoint of $BC$ and $P'$ the midpoint of B'C'. Also, $|AP| = |A'P'|$ and $|AC| = |A'C'|$ and $\angle CAB$ = $\angle C'A'B'$. $2|AP| > |AC|$ ...
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1answer
24 views

Solve an Angle-Side-Angle special case triangle if it has an obtuse angle?

I've seen this type of problem multiple times on homework, and it's confusing me like mad. The scenario: We have a triangle. It is a special case triangle, with one angle, one side, and another ...
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2answers
16 views

How to find opposite and adjacent lengths of a right triangle given the hypotenuse and angle?

I'm writing a few functions for a JavaScript game engine. Is it possible to calculate the length of the legs of a right triangle given ONLY the length of the hypotenuse and an angle?
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Is the centroid of any triangle can be calculated by averaging vertices

Is it always true that the centroid of any triangle can be calculated by averaging the x and y coordinates of its vertices without bothering with finding medians?
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3answers
71 views

Finding circumcentre

Tangents are draw from $P(2,3)$ to $x^2+y^2=4$ meeting at $Q,R$ on circle. Parallelogram $PQSR$ is completed. Find the circumcentre of triangle $QSR$. My attempt: Clearly, the parallelogram is a ...
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1answer
31 views

Find out the $\angle PRQ$

please, help me to solve this.How can I proceed.I just need help. $PQR$ is a triangle. $M$ is a point on $QR$.here,$QM=1/3RM$ , $\angle RPM=30^ \circ$ and $ \angle QPM=20^ \circ$ now,$ \angle PRQ=??$ ...
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1answer
30 views

Orthocentre of a triangle defined by three lines

Problem: If the orthocentre of the triangle formed by the lines $2x+3y-1=0$,$x+2y-1=0$,$ax+by-1=0$ is at the origin, then $(a,b)$ is given by? I would solve this by finding poins of intersection and ...
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4answers
53 views

Mathematics based on triangles

How to find the third cordinate of a triangle , where as other two points are known. and a angle is known. Lets say , the two points are (0,0) , (600,0) and we need to find the third cordinate . ...
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1answer
13 views

Obtaining consistent triangle surface normals.

I am given 3 points in a random order like so... calculateSurfaceNormal(point1, point2, point3); I have implemented the method by simply saying... ...
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1answer
23 views

Change in length of a right triangle

And so my question is how do I prove the ??
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1answer
54 views

Locus of the centres of equilateral triangles (contest problem)

Given a triangle $A_0A_1A_2$ determine the locus of the centres of the equilateral triangles $X_0X_1X_2$ satisfying the condition that each of the lines $X_kX_{k+1}$, $k=0,1,2$ passes through ...
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1answer
39 views

Geometry/Programming- Draw An Equilateral Triangle Given One Point And A Desired Rotation

I feel this question has a stronger mathematical basis than strictly computer science. I am currently drawing an equilateral triangle given its center and its radius like so. I would like to ...
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2answers
35 views

Does the median make angles in the same proportion as the sides?

Till I remember I had studied this in the lower classes, but am not sure whether this is true or not. In the figure CD is a median. Does CD divide the angles 1 and 2 in the same ratio of the sides a ...
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0answers
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How to calculate normal (of magnitude 1) of a triangle?

I am currently doing a bit of geometry practice and wanted to know how to calculate the normal (of magnitude 1) of a triangle defined by 3 vertices: a, b and c`. ...
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3answers
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Making 7 vertices triangle free graph bipartite by deleting an edge

Can anyone assert or refute the following claim? Claim: In every triangle free undirected graph $G=(V,E)$, $|V|=7$, there exist an edge $e\in E$ such that $G'=(V,E\setminus\{e\})$ is ...
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3answers
69 views

Perpendicular lines inside and outside a circle

No trigonometry allowed. Let $\Delta ABC$ be inscribed inside a circle.Let $P$ be a point on the circle.Let $PD$ and $PE$ be perpendiculars on on $BC$ and $AC$ respectively.Let $DE$ when extended ...
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2answers
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Solving a triangle using the given equation

In a triangle $ABC$ $2a^2+4b^2+c^2=4ab+2ac$ then the numerical value of $cos B$ equals ? ($a,b,c$ are sides opposite to angles $A,B,C$) I tried to use cosine rule , but couldn't adjust terms ...
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2answers
35 views

Unusual result when comparing trigonometry and Pythagoras in triangles.

I'm a Scottish Higher maths student. I was looking over some old textbooks, and came across a seemingly easy question, involving a circle within a triangle. I used the expected method to solve it; ...
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15 views

Optimally connecting 2D points to form as many nested triangles that do not overlap

So I have 3 cities that are pretty far apart (2D plane). Distance between each of them more than 50km. In every city I have nodes scattered throughout the city in a random fashion. I know the 2D ...
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1answer
23 views

Computing distance in circle

It seems to me as pretty simple, but I just can't get hold of it: I am trying to compute fn(x, r). Thanks.
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1answer
24 views

Triangle and Vectors.

In triangle $\triangle ABC$, If $(\overrightarrow{AB}-3\overrightarrow{AC}) \perp \overrightarrow{CB}$, what is the largest value can angle $\angle BAC$ attain?
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1answer
34 views

Incenter of Triangle in 3D

I'm trying to figure out how to find the incenter of a triangle with (x, y, z) coordinates for the verteces. I can find the lengths of the sides and the radius of the incircle from that, so I've ...
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2answers
111 views

Find the area of shaded triangle inside of a rectangle.

In rectangle $ABCD$, $ P$ is the mid point of $AB$. $S$ and $T$ are the points of trisection of $DC$. If area of the rectangle is $70$ square units, with reference to the figure find area of shaded ...
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2answers
45 views

Given length of two medians and one altitude , find the length of one side.

In $\triangle ABC$, altitude $AD = 18$, median $BE = 9\sqrt5$ and median $CF = 15$. Find $BC$. (Note that I've drawn median AG) By appolonius theorem , $$2(15)^2+ 2x^2=(2y)^2+(2z)^2$$ ...
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2answers
37 views

Knowing the length of two sides of a triangle and the angle bisector in between , find the length of one of the altitude.

In $\triangle ABC$, $AB = 6, AC = 8$ and internal angle bisector $AD = 6$ such that $D$ lies on segment $ BC$. Compute the length of altitude $CF$ where $F$ is a point on line $AB$. For calculating ...
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2answers
47 views

Three sides of a $\triangle$ are known. If a circle with it's center on base of $\triangle$ touches the other two sides , find the radius of circle.

In $\triangle ABC$, $AB = 10, AC = 12$ and $BC = 18$. A circle is drawn such that its center is on side $ BC$ and it touches lines $AC$ and $AB$. Find the radius of the circle. By pythagoras ...
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5answers
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How to calculate the area of a triangle ABC when given three position vectors $a, b$, and $ c$ in 3D?

Where $a = ( 0, 1, 3), b = (2, 1, 4)$, and $c = (1, 3, 2). $
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2answers
48 views

Area of the given triangle

Through an arbitrary point lying inside a triangle, three straight lines parallel to its sides are drawn. These lines divide the triangle into six parts, three of which are triangles. If the areas of ...
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0answers
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Force to change the base length of an isosceles triangle

Given an isosceles triangle with legs 7' long weighing 160lbs. What horizontal force would be required to change the base width from 15' to 13'? The ends are on wheels-so assume perfect conditions ...
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2answers
62 views

Angle bisector divides the triangle into two triangles. Find the area of one of them.

In $\triangle ABC, AB = 12, AC = 10$. $I$ is incenter $∠BIC = 105 ^{\circ}$. Find area of $\triangle ABD$ where $AD$ is angle bisector. I've drawn the following figure: Now, $∠IBD + ∠ICB =75 ...
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1answer
22 views

If an equilateral triangle has an area of 36 units squared, what is the length of a side to the nearest tenth?

I have been working with finding the area of a regular triangles, squares, and hexagons using special right triangle formulas drawn from the radii and apothems, but I cannot for the life of me work ...
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1answer
161 views

Series for envelope of triangle area bisectors

The lines which bisect the area of a triangle form an envelope as shown in this picture It is not difficult to show that the ratio of the area of the red deltoid to the area of the triangle is ...
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1answer
39 views

Show that for triangle ABC, with complex numbers for the coordinates, that we have the following equation

so I am doing an assignment on triangles and complex numbers, but I am stuck in the very first question. I am not asking for the solution, I would just like a hint or some ideas on what I need to look ...
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2answers
70 views

How to prove that $\frac{r}{R}+1=\cos A+\cos B+\cos C$?

How do we prove that for any triangle this holds: $$\frac{r}{R}+1=\cos A+\cos B+\cos C$$ I can use this beautiful identity to prove several geometric inequalities, but I have no idea how to prove the ...
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1answer
24 views

Reverse triangle inequalities with three elements

Could you help me to show that $$ |a-b-c|\geq |b|-|a|-|c| $$ ?
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1answer
39 views

Finding ratio of external division in a triangle.

Given a $\triangle ABC$ and $P$ dividing $AB$ internally in the ratio $2:3$ $Q$ dividing $AC$ internally in the ratio $1:2$ , with $PQ$ produced and $BC$ produced intersecting in $R$ , to find the ...
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2answers
42 views

triangle construction given side, angle and median

I can't figure out the solution to this, it looks to me like it doesn't have any solution but I need some proof. problem: Construct a triangle ABC with given $a=6 cm$ $\alpha=75^\circ $ and ...
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2answers
85 views

Given the length of two altitudes and one side , find the area of triangle.

Segments $BE$ and $CF$ are the altitudes in $\triangle ABC$. $E$ is on line $AC$ and $F$ is on line $AB$. $BC = 65$, $BE = 60$ and $CF = 56$. Find $A(\triangle ABC)/100$. By the Pythagorean ...
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3answers
54 views

In $\triangle ABC$, I is the incenter. Area of $\triangle IBC = 28$, area of $\triangle ICA= 30$ and area of $\triangle IAB = 26$. Find $AC^2 − AB^2$

In $\triangle ABC$, I is the incenter. Area of $\triangle IBC = 28$, area of $\triangle ICA = 30$ and area of $\triangle IAB = 26$. Find $AC^2 − AB^2$. Here is a sketch that I drew: From the given ...
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4answers
54 views

Midpoints of a triangle [closed]

The points $(4,2), (-1,-3)$, and $(-10,6)$ are the midpoints of the sides of triangle $ABC$. What is the area of triangle $ABC$?
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1answer
23 views

triangle with given 2 medians and 1 side

I need help with this exercise I got. We have a triangle with given medians ma=6, mb=9 and side (without given median on that side) c=6. What is the length of a and b and with what values of ma,mb ...
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2answers
49 views

A question related to triangles , areas , ratio of areas of triangles.

I know the title is confusing but that is because of 150-character limit, if anyone of you can improve it , please do. Consider $\triangle ABC.$ Choose a point $D$ on segment $BC$ such that ...
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0answers
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How to prove that $FC/FA + GC/GA= 0$ from this triangle problem?

In triangle $ABC$, a transversal line intersects $AB$, $BC$, $CA$ at $D,E,F$ respectively. $BS$ intersects $AC$ at $G$, where $S$ is the intersection of $AE$ and $CD$. How to prove that ...
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2answers
62 views

A problem related to circle , altitude , triangle.

Consider a $\triangle ABC.$ Draw circle $S$ such that it touches side $AB$ at $A$. This circle passes through point $C$ and intersects segment $BC$ at $E.$ If Altitude $AD ...
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2answers
129 views

In △ABC, median AM = 17, altitude AD = 15 and the circum-radius R = 10. Find BC^2

Question is as per title. Here is a sketch that I made : By Pythagorean theorem , DM is 8. Now how can I calculate BD and MC? I still haven't found a way to utilize the information that the ...
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2answers
55 views

why a^2 + b^2 = c^2 in right-angled triangle [duplicate]

a^2 + b^2 = c^2 what is the demonstration of this rule with triangle which has 90 deg? can be proofed using geometry?