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

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7 views

Unable to distinguish between intercepted arc and angle of triangle

$\triangle{PQR}$ is inscribed in circle C such that the measure of $\angle{PRQ}$'s intercepted arc is $70^o$ and m$\angle{PQR} = 50^o$. Find the measure of $\angle{QPR}$'s intercepted arc. When I ...
1
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0answers
9 views

Let $T_1$ and $T_2$ be two circumferences…

Let $T_1$ and $T_2$ be two circumferences with centers $O_1$ and $O_2$ respectively, such that $T_1$ passes through $O_2$. Let $C$ be a point on $T_1$. Let $r_1$ and $r_2$ be the lines tangent to $T_2$...
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0answers
13 views

Geometry Of Unitary Transformations

Ever since I first took Linear Algebra, I have over time realized how concepts like determinants, eigenvalues, diagonalization, orthogonal transformations and so on have very intuitive geometric ...
1
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1answer
11 views

Ratio of bisected cevian in triangle given intersection point

I have the coordinates of points $A$ $B$ and $C$ that form triangle $\triangle ABC$, and the coordinates of a point $D$ inside of $\triangle ABC$. Imagine a cevian, connecting points $A$ and $D$, and ...
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2answers
22 views

How many solutions exist for the intersections of these two line? Analytic Geometry

These are the questions I, just want to make sure i did the steps correctly 1.How many solutions exist for the intersections of these two line? (x,y)=(1,6)+s(3,-2) (x,y)=(4,4)+t(-6,4) 2.Find the ...
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1answer
47 views

If $a^2+b^2 = c^2$ and $a,b,c$ are sides of a triangle, can we say the triangle is a right triangle?

This may in fact be a silly question. Pythagoras tells us that $a,b,c$ are sides of a right triangle, then $a^2+b^2=c^2$. But is the converse true, that is if $a,b,c$ are sides of a triangle such ...
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1answer
25 views

Taylor's Theorem for $C^{\infty}$ functions

I am reading Tu's Introduction to Manifolds, the part where he derives a Taylor theorem (with remainder) for $C^{\infty}$ functions for points that belong in a set U that is star shaped with respect ...
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1answer
16 views

How to find the corresponding 2D Cartesian coordinates from 3D ellipsoid?

I want to implement trilateration algorithm in short distance (maximum 50 meters), so instead of calculating intersections among spheres, I can roughly deal with it as finding intersections among ...
2
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1answer
57 views

How to calculate the ABV of an alcohol-infused watermelon?

I am trying to calculate the approximate ABV (alcohol by volume) of a watermelon that I am saturating with vodka. Details If I were to cut the watermelon in half length-wise, its face would be an ...
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0answers
5 views

Oblique projection onto orthogonal complement

I'm looking for an expression for the oblique projection along $B$ onto the orthogonal complement of $C$. Simply modifying the well-known oblique projection formula for the oblique projection anlong $...
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0answers
10 views

Getting starting/endings points Related to Displacement Vector

I am using this resource to calculate the distance between two 3d line segments. At the end it provides the 3D Vector dP. The length of this vector provides the correct distance between the two lines ...
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1answer
38 views

Distance between points on a circle [on hold]

A, B, C, D are points on a circle with AB=5 cm, BC=12 cm, AC=13 cm and AD=7cm. What is the closest approximation of CD?
2
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0answers
29 views

Iterating three tangent circles using Malfatti Circles

First, construct three tangent circles (blue circles), then construct the triangle joining their centers. Then construct three Malfatti Circles for this triangle (green circles). Go on. What I'm ...
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0answers
36 views

Three disks unique intersection contained in another circle

Let three disks:(assume a disk is the set of points of distance at most r from a center point) one centered at a with radius r_a, One centered at b with radius r_b, And one centered at c with radius ...
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0answers
41 views

Calculate lesser value that can take the side c=? [on hold]

EDIT: Consider a right triangle , it is satisfied that: $ab + bc + ac = 100$ Determine the smallest value that can take the side c (without brute force)
-3
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0answers
32 views

Comp Questions-Enumeration, Rates, Numbers, Geometry [on hold]

For each integer from 0 to 999, Michael wrote down the sum of its digits. What is the average of the numbers that Michael wrote down? It takes Jacob one and a half hours to paint the walls of a room ...
5
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1answer
131 views

Israel tst 2011 geometrical inequality

Inside an equilateral triangle of area $S$ lies a point, whose distances to the vertices are $x,y, z$. Prove that $xy + yz + zx \geq \frac{4}{\sqrt{3}} S$ I haven't got any idea yet. But I guess ...
2
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0answers
20 views

Covariance Matrix of Uniform Distribution Positive Definite

Suppose that $B$ is a Lebesgue measureable subset of $\mathbb{R}^d$. Let $U$ be the uniform distribution on $B$. Let $x \sim U$, and let $M = \mathbb{E}[xx^T]$. What conditions on $B$ guarantee that $...
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3answers
17 views

Cubic centimeters

Simple question which applies to chemistry in a measurement context as i am trying to understand centimeters cubed. If we calculate a box's volume. The width, length and height of a box are $15.3, 27....
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0answers
32 views

Get user position on the viewport

I'm creating a game, and I want to get the user x and y position on the viewport, but the problem is, I only have the world size and the viewport size and the user position based on the world. I made ...
1
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1answer
50 views

I need someone to explain this shape to me.

The hexagon fits in the circle perfectly, the circle fits in the square perfectly. but the hexagon doesn't fit in the square perfectly. Doesn't this defy this formula below? a = b b = c a = c (what ...
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1answer
42 views

Why does $2\pi$ divided by the number of sides of a polygon give a regular polygon?

If I have $2\pi/n$, where $n$ is the number of sides of a polygon, does the answer give me a length of sides necessary for me to draw the polygon with those $n$ sides as a regular polygon inside the ...
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0answers
14 views

Getting points Related to Displacement Vector

I am using this resource to calculate the distance between two 3d line segments. At the end it provides the 3D Vector dP. The length of this vector provides the correct distance between the two ...
1
vote
2answers
47 views

Let ABCD be a parallelogram and let M be a point…

Let ABCD be a parallelogram and let M be a point on side AB. Let P be the intersection of side BC with the parallel line to AC that passes through M. Let Q be the intersection of AC with the parallel ...
0
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0answers
20 views

What do you call the projected curve of a circle/ellipse on a cylinder?

What do you call the projected curve of a circle/ellipse on a cylinder? (The figure shows a circle projected on a cylindrical surface) See Figure (Circle Projected on a Cylinder) EDIT: If a name ...
2
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4answers
33 views

How to know if a segment is completely included between two lines?

I have three segments (not necessarily parralel): blue $((ax1, ay1), (ax2, ay2))$ green$((bx1, by1), (bx2, by2))$ red $((cx1, cy1), (cx2, cy2))$ and a $margin$ value which is the width of the sky ...
2
votes
1answer
66 views

Volume of the ellipsoid $(x+2y)^2+(x-2y+z)^2+3z^2=1$

Find the volume of the ellipsoid $(x+2y)^2+(x-2y+z)^2+3z^2=1$, using integration. It is clear that this is not centered at the origin. So, how do I find the limits for an integral? Any suggestion ...
1
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1answer
37 views

Is this a correct question?

Q. Find the shortest distance between two non-intersecting lines passing through the points whose position vectors are a and b are parallel to vectors c and d respectively. My confusion is : two non-...
0
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1answer
43 views

Geometry Proof : How to prove that $BV$ and $CT$ are perpendicular

Let $ABC$ be a triangle. We construct squares $ABST$ and $ACUV$ with centers $O_1$ and $O_2$, respectively, as shown. Let $M$ be the midpoint of $\overline{BC}$. (a) Prove that $\overline{BV}$ and $\...
2
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1answer
36 views

Geometric Intuition of Group Structure on Elliptic Curve

I am reading Number Theory 1: Fermat's Dream by Kato. In Chapter 1 he defines the group structure on a general elliptic curve $$y^{2} = ax^{3} + bx^{2} + cx + d$$ (where $a \neq 0$, and the cubic ...
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1answer
38 views

Let D be the midpoint of BC in triangle ABC. Let E be the midpoint AD, F be the intersection of line BE with side AC. Find $\frac{AF}{FC}$.

Let D be the midpoint of side BC in triangle ABC. Let E be the midpoint of line AD and let F be the intersection of line BE with side AC. Find $\frac{AF}{FC}$.
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1answer
30 views

Given a point, a vertex or covertex, and the center, how do you find the equation of the ellipse?

Say you have three points, P, V, and C. Point V is a vertex or covertex of the ellipse we're trying to find, point P is a random point on the ellipse, and point C is the center of the ellipse. For ...
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2answers
43 views

Find area of this circle

Given the circle O with perpendicular diameters and a chord, find the area of the circle if $EF = 8"$ and $DE = 20"$ inches.
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0answers
51 views

Is there a way to solve this problem of Euclidean geometry , with analytic geometry or vectors?

The problem is a imo's problem. Triangle ABC has circumcircle H and circumcenter O. A circle R with center A intersects the segment BC at points D and E, such that B, D, E, and C are all different and ...
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1answer
49 views

Formula for number of faces in 4 dimensions

If a polytope has $m$ faces in 3 dimensions, how many faces does its analogous polytope have in four dimensions? Does a formula exist? For example, if $m=4$, you have a tetrahedron, and the 4-...
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1answer
21 views

minimization on a u-shape curve

There is a function y=f(x), f'(x)<0, for all values of x. There is another function y=g(x),g'(x)>0, for all values of x. There is a third function y=h(x), which is u-shaped. We assume that both f-h ...
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1answer
23 views

Three vertices of a rectangle are (-4,5), (-4,2) and (3,2). Plot these points and find the coordinates of the fourth vertex. [on hold]

This question forms part of Coordinate Geometry There are three vertices of a rectangle, namely: $$A(-4,5), B(-4,2), C(3,2)$$ How would I plot these points and find the coordinates of the fourth ...
4
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0answers
61 views

Citing Math Proofs.

I am writing a math paper on which $p$-gons are constructible by compass and straightedge and the construction of the $17$-gon. I am taking many proofs (but writing them in my own words) from a book, ...
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0answers
19 views

Can a section of a signed distance filed uniquely determine this field function?

A Signed distance field function is a field function which tells the minimum distance from any point in space to a specific object. Let $\phi(\vec{x})$ be a signed distance field function, an ...
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2answers
34 views

How to rotate a line based dimensions of a piece of paper

I have a line where I know the start and end point on a piece of paper with the dimensions of 8 1/2 inches x 11 inches. the start point is 5.6 inches from the right of the paper and 4 inches down ...
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1answer
36 views

a solid geometry problem

In the following 3D figure, we know that $AE \bot EC, AD \bot BD$, how to prove that $|ED| < |BC|$ ?
4
votes
2answers
65 views

What algebra is generated by $\mathrm{O}(2)$?

The unit complex numbers can be identified with the $2 \times 2$ special orthogonal matrices $\mathrm{SO}(2)$. The problem with $\mathrm{SO}(2)$, however, is that its not closed under $\mathbb{R}$-...
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2answers
55 views

Decomposition to rotation around arbitrary axis

In 3d, I have a $4\times4$ matrix $M$, which has only a rotation part and a translation part. In other words, I can compute $X'=RX+T$ ( with $R$ a $3\times3$ rotation matrix, $T$ a vector for the ...
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0answers
48 views

Find the length of the side of a right angle triangle inside a circle

Hello Stack Exchange. I have a question which has really been preventing me from making a certain program.In my program I need to find the length of AC using only AB and BD.The triangle is right-...
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1answer
44 views

Complex Number Application in Isosceles Triangle Incentre

On the Argand plane $z_1, z_2$ and $z_3$ are respectively the vertices of an isosceles triangle ABC with AC = BC and equal angles are θ. If $z_4$ is the incentre of the triangle then prove that $(...
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1answer
34 views

Permutations of geometric structure

Sorry about the title, i don't know how to describe this problem. I tried counting my way through this problem but kept getting the wrong answer(which is 12, by the way). Is there a more systematic ...
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0answers
14 views

More generalization of the Sawayama lemma

Let $ABC$ be a triangle, $P$, $Q$ be two isogonal conjugate. $AP$, $AQ$ meets (ABC) at $D, E$ respectively. Two lines through $D, E$ meet (ABC) at $T, N$ and meet BC at $G, H$ respectively. Let $PG, ...
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2answers
43 views

How to solve the question related to geometry.

The question is : If $AB$ and $CD$ be two chords of a circle meets at $E$ then show that $\frac {AE} {CE} = \frac {DE} {BE}$. I don't find any clue to solve it.Please help me.Thank you in advance.
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0answers
43 views

Variant of Barrow's inequality

I proposed the conjecture as following: Let $ABC$ be a triangle, let $D$ be a point inside of $ABC$. From $D$ and $ABC$, define $F$, $E$, and $G$ as the points where the internal angle bisectors of $\...
2
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2answers
35 views

proving that triangles $ABC$, $A'B'C'$ are congruent

Given $AD$ is a median to $BC$ in triangle $ABC$, and $A'D'$ is a median to $B'C'$ in triangle $A'B'C'$, and $AD=A'D', AC=A'C', AB=A'B'$. How can i prove that triangles $ABC$, $A'B'C'$ are congruent? ...