For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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0
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2answers
14 views

Problem of bodies in motion in circles.

Consider two circles of radii $4\;cm$ and $8\;cm$, respectively, both circles have the same center $C$ and is two bodies $A$ and $B$, so that $A$ is smaller circumference of the trajectory at a ...
0
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1answer
17 views

Finding out co-linear points

How many triangles with positive area can be drawn on the coordinate plane such that the vertices have integer coordinates $(x,y)$ satisfying $1≤x≤3$ and $1≤y≤3$? It is easy that we have ...
1
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1answer
13 views

Function on plane with incenter

Let $f$ be a function from the set of all points on the plane to the nonzero real numbers. Suppose that for any triangle $ABC$ with incenter $I$, we have that $f(I)=f(A)f(B)f(C)$. What are the ...
0
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1answer
17 views

Hypotenuse and angle ratio relationship

In triangle ABC $\angle BAC=90$, $\angle ABC$:$\angle ACB $=1:2 and AC = 4cm. Calculate the length of BC. I tried this by constructing an equilateral triangle as in the figure. I am interested in ...
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1answer
22 views

What > should the radius of the tank be if it is to be of the largest possible volume?

A certain rectangular crate measures 8 feet by 10 feet by 12 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its ...
2
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3answers
36 views

if the third vertex lies on the line 4x+3y-12=0, find the area of the triangle [on hold]

the vertices of the base of an isosceles triangle are $(-1,-2)$ and $(1,4)$ . if the third vertex lies on the line $4x+3y-12=0$, find the area of the triangle.
2
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0answers
23 views

Rotating a cube about an axis through opposite vertices

I have a cube made using CSS transforms that I'm trying to animate rotating about an axis going through 2 opposite vertices. What I have: Initial cube: ...
0
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0answers
17 views

How prove this $\angle PK_{3}B=\angle BK_{3}Q$

Question: three circles $K_{1},K_{2},K_{3}$ are tangent to each other,(Circles $K_{1}$ and $K_{2}$ are externally tangent at a point $T$),Denote by $L_{1}$ is the exterior common tangent of the ...
1
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2answers
26 views

Given two circles, find the length of a pulley belt that connects the two.

So the problem is that there is one circle with radius of five and one circle with radius of 1. There centers are 8 units apart and there is a pulley belt that goes around the outside as shown in the ...
0
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0answers
29 views

there exists a unique plane in a point of a surface in $\mathbb{R}^3$ [on hold]

The question is how I can prove the existence in this problem: If $M\subset \mathbb{R}^3 $ is a smooth surface. Then, there exists a unique plane $\Gamma\subset \mathbb{R}^3$ that passes through ...
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2answers
21 views

Having a bit of trouble with min/max distance from sphere to point

The sphere is $x^2 + y^2 + z^2 = 81$ and the point is $(5,6,9)$ I am using Langrane multipliers , but the answers I am getting are so far off. I will post my system of equations soon. I found ...
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3answers
43 views

Dividing line segments with ratios vs. fractions [on hold]

I know that $2:3$ is actually $\frac {2}{3}$. So when you split a line segment by a ratio, you would add $2$ and $3$ to get a fraction of $\frac {2}{5}$ that will be used to solve the problem. I ...
1
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0answers
25 views

System of quadratic equations for a tetrahedron

I know the dimensions of the base of a tetrahedron and the angles between the non base sides at the apex. I want to know the lengths of the three non base sides. Let the base's corner points be $A, ...
2
votes
2answers
25 views

How to find perpendicular point of a vector to another vector 2d

Given the axis x-y and some random points to the vectors AB and CD, how can i find out where will the point D lie when the vector CD(dashed line) is perpendicular to AB. For example if point A has ...
0
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1answer
21 views

Why does the focus point distances of an ellipse sum up to the length of the major axis diameter

Why does the distances from the focus points of an ellipse to arbitrary point in the ellipse sum up to the length of the diameter of the ellipse in the major axis? In other words, how to prove: I ...
0
votes
1answer
15 views

Translation of basis for a vector space on the specified distance

In the Euclidean space $XYZ$ is a basis $X_1Y_1Z_1$ defined that is specified by the vectors $\overrightarrow {O_1X_1}$, $\overrightarrow {O_1Y_1}$ and $\overrightarrow {O_1Z_1}$. How to calculate ...
2
votes
1answer
15 views

Weighted average of multiple points

Let's say I have a triangle whose three corners are $$(x_1,y_1),(x_2,y_2),(x_3,y_3).$$ I have a weight assigned to each one as a percentage, so the first point might be $75\%$, the second $15\%$ and ...
1
vote
1answer
34 views

Lines joining origin to points of intersection of two conics

If the lines joining origin and point of intersection of curves $$ax^2+2hxy+by^2+2gx=0$$ and $$a_1x^2+2h_1xy+b_1y^2+2g_1x=0$$ are mutually perpendicular, then prove that $$g(a_1+b_1)=g_1(a+b)$$ How ...
1
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3answers
38 views

Meanings of Sine, Cosine, Tangent

Whenever I have a question dealing with sine, cosine, and tangent, my teacher always says to use a calculator. I would like to know how you would solve these without just using a calculator, that way ...
1
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0answers
13 views

Trig equation that fits the plot points (octagonal pyramid)

I'm looking for an equation that satisfies these conditions: Input 90 degrees, result is 90 degrees Input 45 degrees, result is 60 degrees Input 0 degrees, result is 45 degrees For an input value ...
4
votes
1answer
44 views

Is the non-existence of a general quintic formula related to the impossibility of constructing the geometric median for five points?

In particular, in the Computation section of in the Wikipedia page for geometric median, there is this statement: ...but no such formula is known for the geometric median, and it has been shown ...
1
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1answer
23 views

How could I calculate the local size of an object given its distance and actual size?

Lets say I take a picture of a sign. I know that sign is 20ft (width), 10ft height. I'm standing 40 feet away. If I were to take a picture, how could I calculate how wide and how high the sign is in ...
0
votes
1answer
21 views

Find the Equation of BC

$\Delta ABC$ with vertex $A(1,2)$ has equations of internal angle bisectors of $\angle B$ and $\angle C$ as $x-y-1=0$ and $2x+y-9=0$ Respectively. Find the Equation of $BC$ My approach: Solving for ...
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4answers
24 views

Find depth of a half-filled parabolic cross-section

Given a cross-section of an object that is parabolic in shape, how do you find the depth of the object when it is "half full". A full example given in an exam: A long trough whose cross-section ...
1
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0answers
69 views

Why does base*height work?

I want to rigorously prove the idea that Base*Height=Area works (I do realise there are shapes which do not satisfy this equation). I think I can see why it works for integer values, but I want ...
-10
votes
1answer
54 views

What's the lenght? [on hold]

Imagine a roll of sheet outer radius R and inner radius r and the thickness dx , what's the length? I'm interested to see how many different solution or approach to this problem exists !
0
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0answers
23 views

How do I compute corners of geodesic rectangle?

I have the center of a rectangle as a latitude and longitude as well as the length of the sides in meters and the orientation in radians. How can I compute the ...
2
votes
0answers
41 views

Geometry - formula for angles in isosceles triangle

EDITED: new picture, less confusion. Please view the picture above. It is an isosceles triangle It is mirror symmetric, all circles are EQUAL in radius. Let the green and purple angles be P and ...
1
vote
1answer
26 views

Find rigid transform from coordinates of the same points in different reference frames

Given two* 3-dimensional points $p_1$ and $p_2$ expressed in different reference frames $A$ and $B$, find the rigid transform (rotation and translation) between frames $A$ and $B$. The answer to this ...
1
vote
1answer
18 views

Axis dimensions of oval around inscribed rectangle

I have a rectangle of known width and height. This rectangle is inscribed in an oval. So, to be clear, the corners of the rectangle are just touching the oval, making the oval as small as possible ...
0
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0answers
11 views

Time of flight for a projectile with stated initial velocity and size at various distances [migrated]

I've been mooching round the internet looking for an answer to this one and can't find a ready resource, hence the question. In short, I'm trying to discover the flight time of a shotgun pellet at ...
0
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1answer
14 views

Medians of a triangle and the sides of the triangle relationship [duplicate]

Suppose the medians of a triangle are 5,12 and 13 units, find the sides of the triangle. I understand that the medians meet and form centroid. But I am uncomfortable to apply this to this problem
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1answer
19 views

I'm looking for two euclidean polytopes such that their cartesian product is no longer a euclidean polytope.

I'm looking for two euclidean convex polytopes such that their cartesian product is no longer a euclidean convex polytope. Does such a thing exist? Note here by convex polytope I mean the set $ K ...
2
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0answers
30 views

Ratio of angles of a right triangle

P.S: I only want a hint,not the whole solution. BdMO 2009 Problem 5 Secondary In triangle ABC, $\angle A = 90$. M is the midpoint of BC. Choose D on AC such that AD = AM. The circumcircles ...
1
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2answers
25 views

calculate circle segment area: determine distance

I have a problem calculating the area of a circle segment. I know how to separate this into smaller tasks (triangle and remaining circle segment) that are basically easily solvable, but one distance ...
0
votes
2answers
53 views

How to find the intersection points of lines that are normal to two curves?

Let I have two curves, \begin{gather} f(x)=\frac{x^3}{4}+1 \\ g(x)=\frac{(x-\tfrac{1}{2})^3}{7}+\tfrac{1}{2} \end{gather} There are zero or more lines that are normal to both curves. In other words, ...
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votes
2answers
92 views

What is the area of a 12cm square? [on hold]

I am working through a maths revision sheet based on measurement and I have come across a question that simply states, what is the area of a 12cm square?
0
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1answer
25 views

Minimal number of points to define a rotated ellipse?

What is the minimal number of points $N$ to uniquely define the semi-major axis $a$, the semi-minor axis $b$ and the rotation angle $\omega$ of an ellipse whose the center is known/fixed (this is ...
3
votes
2answers
83 views

The relationship between two definitions of star-shaped domain

There are two definitions of star-shaped domain. One is given in wikipedia as follows. Def1: A set $S$ in the Euclidean space $\mathbb{R}^n$ is called a star domain (or star-convex set, star-shaped ...
-1
votes
1answer
41 views

How to get the third point coordinates in isosceles triangle?

Isosceles triangle $ABC$ $AB = AC = d_1$ $BC = d_2$ $A = (x_1, y_1)$ $B = (x_2, y_2)$ $C = (x_3, y_3)$ $\angle BAC = \phi$ $\angle ABC =\angle ACB = \theta$ I want an equation for $x_3$ and $y_3$ ...
1
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0answers
23 views

How prove that $(DB+BC)^2=AD^2+AC^2$ in convex quadrilateral?

Let ABCD be a convex quadrilateral,and write $\alpha =\angle DAB,\beta =\angle ADB,\gamma =\angle ACB,\delta =\angle DBC , \epsilon =\angle DBA. $ Assuming that $\alpha <\frac{\pi}{2},\beta +\gamma ...
11
votes
5answers
233 views

Unit circle is divided into $n$ equal pieces, what is the least value of the perimeters of the $n$ parts?

A unit disk is divided into $n$ equal pieces, that is, each piece has area $\dfrac\pi n$. equal "pieces" means equal area Let $l_1, l_2,\dotsc,l_n$ be the perimeters of the $n$ parts, ...
0
votes
1answer
31 views

Show that every imaging f with certain properties is a group

Let $f:\hat{C}\to\hat{C} $ a bijection with the property to sent lines an circles to lines and circles. Show that f is a group with operation the composition of functions (images) (whom obviously ...
2
votes
1answer
26 views

Is it possible that the fact the number of inflection points is zero changes in some different coordinate system?

Let $L$ be a line segment in the $3D$ Euclidean space. And Let $L_{xy}$ and $L_{xz}$ be the projections of $L$ onto the $XY$ and $XZ$ planes, respectively. Assume both of $L_{xy}$ and $L_{xz}$ have no ...
0
votes
1answer
40 views

? Confocal ellipses and hyperbolas cover whole Euclidean plane

I need a proof that we can use confocal ellipses and hyperbolas, with given foci and given perpendicular bisector of the the line segment between the foci and given pair of rays prolonging the line ...
2
votes
1answer
48 views

Help with simple rotation on an x,y plane

I'm a programmer, with too little background in mathematics, and I am currently faced with the challenge of rotating an object on a 2 axis plane. Something that is hopefully quite easy for you guys. ...
0
votes
0answers
21 views

Angle of a complicated triangle [duplicate]

what is the magnitude of $\angle DEB$? I tried this puzzle with angle sum property of triangle. I could not arrive at the solution
0
votes
1answer
39 views

Number of triangles formed by all chords between $n$ points on a circle

We have $n$ point on circumference of a circle. We draw all chords between this points. No three chords are concurrent. How many triangles exist that their apexes could be on circumference of ...
0
votes
1answer
14 views

About the interior ball condition of a convex set with C^1 boundary

Let $\Omega$ an open bounded and convex domain in $R^n$. Suppose that the boundary of this set is $C^1$. Then $\Omega$ satisfies the interior ball condition for all boundary points? Intuitively ...
1
vote
1answer
41 views

problem about length of perpendicular chords

Question $AB$ is chord of circle $O$,points $D$ and $E$ are chosen on $AB$ in a way that $AD=BE$.prove two chords that are perpendicular to $AB$ and pass $D$ and $E$ points are equal.(prove $LK=MN$) ...