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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0answers
8 views

Describe curves by words

I am trying to describe the general aspect of the following curves My ideas: The curves are continuous, and defined for positive values of x, and giving negative values. Have logarithmic growth ...
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1answer
9 views

Find the equation of locus of a point which is at a distance $5$ from $A$ $(4,-3)$

Find the equation of locus of a point which is at a distance $5$ from $A$ $(4,-3)$. Could some explain how to solve this in detailed.
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1answer
24 views

Two tangents BC and BD are drawn. Prove that Ob=2BC

Two tangent segments BC & BD are drawn to a circle with centre O such that $\angle$CBD=120$^{\circ}$. Prove that OB=2BC. What I've tried, BC=BD[two tangents drawn from a single point to the ...
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0answers
26 views

Prove an geometry related equation.

$\Delta ABC$ is an isosceles triangle. $\angle BAC$ is an right angle. $BC$ is its hypotenuse and $P$ is any point on $BC$. Prove that, $PB^2+PC^2=2\times PA^2$. I have tried it in many ways and ...
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1answer
15 views

ABCD is a square of side 4cm. E is a point in the interior of the square such that CED is equilateral. Then find the area of ACE in sq.centimeters.

The given answer is $4*(\sqrt{3} - 1)$ I tried all the methods but could not match the answer. Please tell if the question is wrong. Thanks in advance.
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1answer
27 views

Move a dot along a path

I have a multi-point path to keep it simple it has three points, A B & C. A = 60,410 B = 127.5,410 C = 195,240 This is the 'template' path, I need to animate a dot moving along this path, lets ...
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2answers
15 views

Spectral theorem for unitary operators T o F

Si $T$ es unitaria y $B$ es una base de $V$ formada por vectores propios de $T$ entonces $B$ es un conjunto ortogonal. If $T$ is unitary and $B$ is a basis for $V$ consisting of eigenvectors of $T$ ...
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2answers
31 views

Third Ailles Rectangle

The Ailles rectangle (named after an Ontario high school teacher, D. S. Ailles) is a rectangle of size $\sqrt{3}\times\sqrt{3}+1$ with three kind of triangles, like below. We have triangle ...
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0answers
30 views

Show that the line $KD$ bisects $\angle{EKF}$

Let $P$ be an interior point of an acute-angled triangle $ABC$. The line $BP$ meets the line $AC$ at $E$, and the line $CP$ meets the line $AB$ at $F$. The lines $AP$ and $EF$ intersect each ...
2
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1answer
21 views

Distance between projections

Let $x,y,z \in \mathbb R^2$ such that $||x|| = ||y||= ||z|| = 1$. Project $z$ onto the lines defined by $x$ and $y$ as follows: \begin{equation} z_x = (z^\text{T}x) x, \ \ z_y = (z^\text{T}y) y, ...
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1answer
21 views

Is the interior of a simple polygon, simply-connected?

This may be trivial, but I want to be sure I understand correctly: Is it true that the interior of a simple polygon is always a simply-connected subset of the plane? I.e, is it eligible for the ...
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2answers
20 views

Algorithm to cover maximal number of points with one circle of given radius

we have a plane with some points on it. We know coordinate of each point apriori. We also have a circle of unit radius. I need an algorithm that determines optimal/sub-optimal position of a circle ...
0
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0answers
15 views

find all straight-lines that goes through a point $p$ in projective and affine space [on hold]

I have an exam tomorrow in projective Geometry and I am lacking of many basic skills. For instance this one: How can I find all straight lines that go through $p$ in the projective space $\Bbb ...
0
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1answer
18 views

How can I prove triangle ABC is congruent to triangle MaMbMc? [on hold]

Ma is a point set halfway on AB, Mb halfway on BC, Mc halfway on CA.
3
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0answers
37 views

How to calculate only the area of the visible parts of a 3D PieChart?

I have created a 3D Pie Chart whose major feat (among the others) is to be rotated: I did it to demonstrate how the visual perception of data in a Pie Chart can be distorted depending on the ...
8
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0answers
47 views

A curious triangle inequality

Let $ABC$ be a triangle. Pick a point $P$ inside the triangle. How would you show that \begin{equation} |PA|+|PB|+|PC|+\min\{|PA|,|PB|,|PC|\}\leq |AB|+|BC|+|CA|. \end{equation}
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1answer
52 views

prove that the quadrilateral $ABCD$ is a square

Given $ABCD$ a quadrilateral such that $AB\parallel CD$ and $\angle ACD=45^0, \angle A=90^0, \angle D=90^0 $ Need to prove that $ABCD$ is a square. I tried to use circles but it didn't help. Any ...
2
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0answers
32 views

Proof of Bernoulli's' result on a construction to divide any triangle into four equal parts with two perpendicular lines.

I have been reading about Jacob Bernoulli and came across this particular contribution of his. Although I have tried my best to search proofs of this result I have had no success so far. Probably this ...
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2answers
49 views

Determining the position of a perpendicular line segment connecting two parallel lines that is equidistant from 2 points

I was given this problem and I can't seem to think of a solution. Here is a possibly helpful graphic: Given two parallel lines (representing the banks of a river) and two arbitrary points $A$ ...
0
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1answer
9 views

$N$ - Dimensional Solid of Revolution.

Ok, so if you take a line, or a group of lines, and rotate them $360$ degrees along their axis, you'll get a $3$-dimensional solid. Is it possible to take a $3$-dimensional figure and rotate it ...
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1answer
39 views

Find the length as a function of $r_1,r_2$

We are given two mutually tangent circles in the plane, with radii $r_1,r_2$. A line intersects these circles in four points, determining three segments of equal length. Find this length as a ...
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0answers
25 views

Intersection of a surface and a line.

I have a surface ($H$) that passes every corner points(one coordinate gets its maximum $1$ while others $0$), such as $(1,0,...,0), (0,1,0,...,0),....,(0,...,1).$ H is characterized by ...
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1answer
16 views

Signed angle difference without conditions

I've got two angles in $0 \leqslant a < 360$ and I need to find the signed difference between them which should be $-180 < \Delta < 180$. Is there a way to calculate the difference with ...
2
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0answers
50 views

Ratios of the major axes of ellipses inscribed in a triangle

I recently came across a question that went something like this: In a triangle with vertices (0,0), (6,0), (2,4) an ellipse is inscribed such that it has the largest area. Now it is dilated, that is ...
3
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3answers
68 views

What's the equation for a rectircle? (Perfect rounded-corner rectangle without stretching on only one dim)

The equation for a rounded square seems to be: $x^4 + y^4 = 1$ You can make the radii smaller by increasing (over the even integers) the exponents in the equation. Here's a picture: Wolfram Alpha ...
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0answers
36 views

Synthetic geometry , angles.I need some ideas

Let $ABC$ be a triangle such that $m(\measuredangle ACB)>30$ and $M$ in the interior of the triangle with $m(\measuredangle BMA)=120, m(\measuredangle BCM)=30$. Let$\{ D\} = AM\cap BC$ and $P \in ...
0
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1answer
29 views

Is the Locus circle?

Locus of points such that sum of it's distances of them from four fixed points remains constant? Is the locus circle? I was not able to solve it as there were four radicals. Is it a theorem?
1
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1answer
19 views

Distance between a point $X$ and a line $2x-y = 1$

I am asked to state a condition for a point $X$ such that the point $X$ is a distance of 10 units from the line $2x-y = 1$, and then find the Cartesian equation of the set of all points $X$ that are a ...
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4answers
66 views

How Many Times The Clock Hands Make an angle Theta?

You might have encountered such a question where $\theta=90^o$ but this a little different and is causing a little problem. I approached this problem in the following matter and solved for $\theta= ...
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2answers
32 views

Area of piece of paper folded around straight line of orientation $\theta$

Imagine drawing a straight line $l$ through the center of a square piece of paper with area $1$. Now fold the paper along that line. Q: What is the function for the area covered by the folded ...
2
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3answers
36 views

How to find position of point that is x unit distant from AB line segment and y unit distant from BC line segment?

I am trying to calculate coordinates of point P, which is x units distant from AB line segment and y units distant from BC line segment. Edit: I am trying to write code for general solution. As ...
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2answers
28 views

Question on geometry related to Trapezium and Isosceles Triangle

In figure $AD\perp DE$ and $BE\perp ED$.$C$ is mid point of $AB$.How to prove that $$CD=CE$$
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1answer
36 views

How to find another solution for two cone intersection?

Lets say we have two cones and they intersect: $$ \sqrt{(x-a_1)^2 + (y-a_2)^2} + a_3 = \sqrt{(x-b_1)^2+(y-b_2)^2} + b_3 $$ And we know one solution $x_1, y_1$ for this intersection. Is there any ...
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0answers
15 views

Property of all k-dimesional shapes

A close friend showed me an intuitive pattern that given a k-dimensional convex polytope P, if one doubles every sidelength to generate a $P'$ it is possible to fit $2^k$ copies of $P$ within the ...
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2answers
27 views

find the lenght of segment in a skew quatrilateral

Let $ABCD$ be rectangle so that $|AB| = x$ and $|BC| = y$. Suppose we fold the rectangle along the diagonal $BD$ so that the planes $ABD$ and $BCD$ will be perpendicular. What is the lenght of $|AC|$ ...
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0answers
22 views

given skew lines $l$ and $m$ find the geometric locus

Suppose we have two skew lines $l$ and $m$. I want to find the geometric locus of points $P$ for which there is not line passing trough $P$ intersecting $l$ and $m$. I know the locus of points should ...
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1answer
26 views

Let $O$ be the center of the circle circumscribed around a triangle $ABC$. Does $C$ belong to the plane where the points $A$, $B$ and $O$ belong? [on hold]

Let $O$ be the center of the circle circumscribed around a triangle $ABC$. Does $C$ belong to the plane where the points $A$, $B$ and $O$ belong?
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3answers
282 views

Why is the surface area of a sphere not given by this formula?

If we consider the equation of a circle: $$x^2+y^2=R^2$$ Then I propose that the volume of half of a sphere of radius $R$ is given by the summation of the circumferences of the circles between the ...
0
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0answers
21 views

Concurrence of lines through triangle midpoints [duplicate]

Suppose that points $A, B, C$ form a triangle and that $A'$ $\in$ $l_{BC}$ and $B'$ $\in$ $l_{AC}$ and $C'$ $\in$ $l_{AB}$ are such that the lines $l_{AA'}$, $l_{BB'}$, $l_{CC'}$ are concurrent at G. ...
1
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1answer
30 views

concentration of volume of hypersphere

I am reading about features of volume of hyperballs, where I see two theorems, Most of the volume of the d-dimensional ball of radius r is contained in an annulus of width $O(r/d)$ near the ...
1
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0answers
38 views

Concurrence through a triangle

Suppose that points A, B, C form a triangle and that A' $\in$ $l_{BC}$ and B' $\in$ $l_{AC}$ and C' $\in$ $l_{AB}$ are such that the lines $l_{AA'}$, $l_{BB'}$, $l_{CC'}$ are concurrent at G. ...
1
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1answer
19 views

Calculate most parallel vector

Let's suppose I have a vector $\vec{a}$ and arbitrary many vectors (in my example two: $\vec{b}$ and $\vec{c}$), which all have a common starting point P. Now I want to find out which of these vectors ...
2
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1answer
69 views

Would you confirm this as a proof to the Pythagorean theorem?

I'm new in mathematics, and trying to build my way up starting by doing simple tasks. My current one is proving the Pythagorean theorem without looking it up. This photo contains my current "proof" ...
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2answers
51 views

Areas of triangles in hexagon

A hexagon $ABCDEF$ with parallel opposite sides is given. Prove that $[ACE]=[BDF].$ (here $[]$ denotes area of triangle) Since the sides are parallel does that mean that it is equiangular as ...
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7answers
1k views

Length of a Chord of a circle

I was wondering about the possible values that the length of a chord of a circle can take. The Length of a chord is always greater than or equal to 0 and smaller ...
0
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2answers
28 views

Geometry-||gm proof

$ABCD$ is a parallelogram in which $P$ and $Q$ are the mid points of the sides $AD$ and $BC$ respectively. If $BP$ & $QD$ intersect the diagonal $AC$ at $X$ and $Y$ respectively then prove that ...
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1answer
28 views

Find both the diagonals with area and side given [on hold]

Side of rhombus $= 65$ cm Area of rhombus $= 1024$ cm$^2$ Find the diagonals of the rhombus.
0
votes
1answer
34 views

Rotation addition with quaternions

My task is: "Describe rotation $S \circ R$ by axis and angle, where $R$ is rotation around $(0,1,1)$ by 90 degrees, and $S$ is rotation around $(1,-1,0)$ by 90 degrees." I should use quaternion ...
0
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0answers
25 views

Prove that $x+y \tan {\frac{(\alpha + \beta)}{2}}=0$ [on hold]

The line joining $A(a\cos{\alpha},b\sin{\alpha})$ and $B(a\cos{\beta},b\sin{\beta})$ is produced to the point $M(x,y)$ such that $AM: BM=b:a$; prove that $x+y \tan {\frac{(\alpha + \beta)}{2}}=0$ ...
0
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1answer
34 views

If the coordinates of the vertices $B$ and $D$ are $(7,3)$ and $(2,6)$ respectively, find the coordinates of the vertices $A$ and $C$.

The sides of the rectangle $ABCD$ are parallel to the co-ordinate axes. If the coordinates of the vertices $B$ and $D$ are $(7,3)$ and $(2,6)$ respectively, find the coordinates of the vertices $A$ ...