For questions about triangles

learn more… | top users | synonyms

1
vote
1answer
38 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=??$ ...
1
vote
1answer
72 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 ...
0
votes
4answers
58 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 . ...
0
votes
1answer
14 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... ...
0
votes
1answer
28 views

Change in length of a right triangle

And so my question is how do I prove the ??
3
votes
1answer
80 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 ...
0
votes
1answer
106 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 ...
0
votes
2answers
39 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 ...
1
vote
0answers
26 views

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`. ...
4
votes
3answers
61 views

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 ...
0
votes
3answers
90 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 ...
1
vote
2answers
15 views

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 ...
4
votes
2answers
123 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; ...
0
votes
0answers
34 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 ...
1
vote
1answer
26 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.
1
vote
1answer
30 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?
5
votes
2answers
194 views

Area of triangle

A triangle is inscribed in a circle. The vertices of triangle divide the circle into three arcs of length 3, 4 and 5 units, then find the area of triangle.
1
vote
1answer
65 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 ...
1
vote
2answers
697 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 ...
3
votes
2answers
60 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 , $$2(15)^2+ 2x^2=(2y)^2+(2z)^2$$ ...
1
vote
2answers
75 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 ...
1
vote
2answers
71 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 ...
1
vote
5answers
173 views

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). $
8
votes
2answers
66 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 ...
0
votes
0answers
23 views

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 ...
2
votes
2answers
85 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 ...
0
votes
1answer
98 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 ...
7
votes
1answer
192 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 ...
0
votes
1answer
50 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 ...
7
votes
2answers
104 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 ...
0
votes
1answer
26 views

Reverse triangle inequalities with three elements

Could you help me to show that $$ |a-b-c|\geq |b|-|a|-|c| $$ ?
1
vote
1answer
52 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 ...
2
votes
2answers
80 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 ...
3
votes
2answers
108 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 ...
4
votes
3answers
64 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 ...
-1
votes
4answers
101 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 $ABC$?
0
votes
1answer
25 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 ...
2
votes
2answers
88 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 ...
1
vote
0answers
24 views

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 ...
1
vote
2answers
70 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 ...
2
votes
2answers
158 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 ...
0
votes
1answer
62 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?
1
vote
0answers
56 views

How to prove these equations base on this following interior and exterior angle bisectors problem?

In the triangle $\triangle ABC$, length of $BC$ is larger than length of $AC$. The interior angle bisector of $\angle C$ intersects $AB$ at $D$; and the exterior angle bisector of $\angle C$ ...
0
votes
0answers
27 views

How to prove that PH is containing midpoint of side MN from this circle and triangle problem?

Given: triangle ABC is acute triangle. M and N are midpoints of AB and BC respectively, while BH is altitude of triangle ABC. Circles AHN and CHM meet at point P. (P is not same with H) How to ...
4
votes
2answers
129 views

In triangle, $\sin\frac{A}{2}+\sin \frac{B}{2}+\sin\frac{C}{2} -1 = 4\sin \frac{\pi -A}{4}\sin\frac{\pi -B}{4} \sin\frac{\pi-C}{4}$

To prove $$\sin\frac{A}{2}+\sin \frac{B}{2}+\sin\frac{C}{2} -1 = 4\sin \frac{\pi -A}{4}\sin\frac{\pi -B}{4} \sin\frac{\pi-C}{4}$$ My approach : $$ \begin{align} \text{L.H.S.} & = ...
0
votes
0answers
20 views

How to prove that P,G, and K are collinear from this triangle problem?

Given: triangle ABC. We choose point Q at AC, P1 and P at BC, and R at AB, such that: AR/RB= BP/PC= CQ/QA= CP1/P1B Suppose G is centroid of triangle ABC, and K= AP1 ∩ RQ. How to prove that P,G, and ...
2
votes
1answer
84 views

What is the converse of the triangle inequality?

It's usual when presenting a theorem to also present its converse. Surprisingly, I've never seen the triangle inequality's converse stated. Triangle inequality: If the sides of a triangle are a, b, ...
1
vote
1answer
34 views

How to prove that:$ BC^2= 3CM^2 + AC^2 $from this triangle problem?

In the triangle $\triangle ABC$, angle $\angle A$ is larger than angle $\angle B$. We choose points $M$ and $N$ at $AB$ such that $AM=MN=NB$. How to prove that: $BC^2= 3CM^2 + AC^2$? Which ...
0
votes
1answer
19 views

what is the measure of angle ECD from this following triangle problem?

In triangle ABC, AB is larger than BC. Then, we choose point E outside the triangle such that BE=BC. We extend line AB to D, such that BD=BC. BF is angle bisector of angle ABC. If DC is parallel ...
4
votes
2answers
61 views

How to prove that the angle between two sides of that triangle is less than 60 degree?

The product of two sides of triangle is equal to 8*(R*r) where R is circumradius of this triangle, and r is inradius of this triangle. How to prove that the angle between two sides of that triangle ...