4
votes
2answers
95 views

Relationship between circles touching incircle

I am trying to derive a relation between radius of those outer circles and radius of the incircle. Those outer circles are tangent to the incircle and respective sides. I have tried and failed ...
0
votes
1answer
27 views

Altitudes of Triangle

I have a triangle defined as 3 lines, each defined by two coordinate points A and B. I have the area of the triangle but need to calculate the 3 altitudes and their respective sides A and B points. ...
2
votes
0answers
64 views

Proving there is no set of five distinct points s.t. every three points are the vertices of a right triangle.

We can see that the following proposition is true. Proposition : Each triangle $ABD, ACD, BCD$ is a right triangle for $$A(0,b,0), B(a,0,0), C(0,0,0)\ \ \ (a\gt 0, b\gt 0)$$ $\iff D$ is either ...
0
votes
1answer
11 views

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 ...
0
votes
2answers
26 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 ...
0
votes
0answers
11 views

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 ...
0
votes
0answers
18 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 ...
2
votes
3answers
73 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 ...
1
vote
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=??$ ...
0
votes
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 . ...
3
votes
1answer
56 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
43 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
36 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
21 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`. ...
0
votes
3answers
70 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
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?
1
vote
1answer
37 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
128 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
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 , $$2(15)^2+ 2x^2=(2y)^2+(2z)^2$$ ...
1
vote
2answers
38 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
49 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 ...
8
votes
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 ...
2
votes
2answers
65 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 ...
7
votes
1answer
163 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 ...
3
votes
2answers
72 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 ...
1
vote
1answer
40 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
44 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
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 ...
4
votes
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 ...
-1
votes
4answers
55 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
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 ...
2
votes
2answers
50 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
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 ...
2
votes
2answers
132 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
57 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?
2
votes
1answer
63 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, ...
5
votes
2answers
104 views

Minimum area of a triangle

In triangle inscribed circle with radius $r = 1$ and one of it sides $a=3$. Find the minimum area of triangle? Ans = 5.4 My reasonings: $BC = a$, $AC = b$, $AB = c$ $AD=AF=x$ $FC=CE=y$ ...
1
vote
2answers
80 views

Three circles with two common points

Let $ABC$ be a triangle of any type and $A_1,B_1,C_1$ the feet of the heights. Denote $M,N,P$ the orthogonal projections of the point $A$ onto the lines $B_1C_1,C_1A_1$ and $A_1B_1$. The circes ...
0
votes
2answers
46 views

Why can I not use an equation using proportions to solve this triangle problem?

It is difficult to see the picture of the problem. The question is "What are the lengths of AC and AB?" What is given is a right triangle, ABC. Angle B is 30 degrees and BC is 7.0 distance. The ...
0
votes
1answer
49 views

Competition math geometry question

The perimeter of triangle ABC is $36$, and its area is $36$. Compute $\tan\frac{A}2 \tan\frac{B}2 \tan\frac{C}2$. I found that the answer is $1/9$, but I was not able to find a reason for this. Could ...
0
votes
1answer
42 views

How to prove that $DE=EF +DG$ from this following triangle problem?

Given a right triangle $ABC$, where $C$ is a right angle. We choose points $G$ at $AC$ and $F$ at $BC$, and $D$ and $E$ at $AB$. We draw right triangles $AGD$ and $EBF$, such that $\angle AGD= ...
1
vote
0answers
33 views

Solution for the value of an angle of a triangle ABC

Find value of angle m< DBC Where $$BD=DC=AC$$ $$2(m\langle BAC)=14(m\langle ABD)=7(m\langle BCD)$$ I tried hard but im out of ideas now, I know the answer is 20 but I want to know how, thanks ...
0
votes
3answers
72 views

Finding area of sector inside an triangle

I have been asked this question from a junior and could not solve the question in a simple way. I am asking help on this platform. For a triangle $ABC$, Points $D, E$ on $AB$, where ...
0
votes
2answers
31 views

To find base and height of an isosceles trangle if sides and area are give

The area of an isosceles triangle is $60cm^2$ and the length of equal side is $13cm$. Find height and base.
4
votes
1answer
114 views

Length of median extended to the circumcircle

A triangle has side length $13,14,15$, and its circumcircle is constructed. The median is then drawn with its base having a length of $14$, and is extended to the circle. Find its length.
2
votes
0answers
82 views

Hijacked Malaysian plane position geometry

Sorry to get geeky in the midst of a tragedy and likely horrible crime, but does anyone know how they got this diagram showing the possible last known positions of the possibly hijacked Malaysian ...
0
votes
1answer
43 views

Maximum perimeter of an isosceles triangle inscribed in the unit circle?

So I have seen this question asked before but with variations (circle of radius 4, and an equilateral triangle) and so I am hoping for an answer on how to do this. After looking around I saw that ...
2
votes
2answers
56 views

Find the maximum angle possible

$P$ is a point on the $Y-axis$ . Find the maximum possible value of $\angle APB$ where $A=(1,0)$ and $B=(3,0)$. Here is how I solved the problem. Suppose $P=(0,k)$ . Then using the cosine formula we ...
1
vote
1answer
27 views

Similar Triangles with proportions

In $\triangle ABC$, $AB=8, BC=7, CA=6$, and side $BC$ is extended to point $P$, so that $\triangle PAB$ is similar to $\triangle PCA$. Find the length of $PC$.
0
votes
1answer
23 views

Representation of a Triangle

In this document, a Triangle is represented as: $$ T(s,t) = B + sE_0 + tE_1\\for~all~(s,t)\in D=\{(s,t):s\in[0,1], t\in[0,1],s+t\le1\} $$ Can someone explain this representation of a Triangle?