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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1answer
14 views

Which points lie on the prependicular bisector of (-1,-6) and (5,-8)

$A$ and $B$ are the points $(-1,-6)$ and $(5,-8)$, respectively. Which of the following points lie on the perpendicular bisector of AB? $P(3,-4)$ $Q(4,0)$ $R(5,2)$ $S(6,5)$ Midpoint of $ AB = ...
0
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2answers
32 views

Find the height of statue.

Standing on one side of a 10 meter wide straight road, a man finds that the angle of elevation of a statue located on the same side of the road is X. After crossing the road by the shortest possible ...
3
votes
2answers
91 views

maximum area of semi-circle in square

I'm struggling the with the following question: Given is a square with length $a$. Now I want to find a semi-circle with the max. area. Looks like this: ...
1
vote
1answer
12 views

Extermal curve for specific problems?

I ran into a quiz question last month. how we can find the Extermal curve for following problem. $$ \int_1^2 \frac {\dot {x}^2}{t^3} dt $$ where $x(1)=2, \ x(2)=17$
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0answers
9 views

What is the isotomic conjugate version of the six point circle of isogonal conjugates?

As it is well known, the pedal triangles of a pair of isogonal conjugates in a triangle share a circumcircle. This is a nice theorem, but is there an analogous version of it for a pair of isotomic ...
0
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2answers
22 views

Is there a term for an “unbounded simplex”?

Is there a general term for regions like $\{(x,y):x>y\}$ and $\{(x,y,z): x>y>z\}$, i.e., regions which are simplexes with one open?
5
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2answers
298 views

Find the area of an irregular cyclic octagon

Find the area of the octagon pictured here I do have some ideas how to solve it, but do not want to write them down here, in order not to affect ideas of others.
1
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1answer
36 views

Is absolute value an one dimensional circle?

A circle is the set of all points that are at the same distance r from a given point in a plane (two dimensions). Similarly, a sphere is the set of all points that are at the same distance r from a ...
2
votes
1answer
23 views

Projected Area of Circle onto the Side of a Cylinder

I have encountered a problem that requires me to find the projected area of a beam of light (circular cross-section, with radius R1) vertically onto the side of a cylinder with R2 as its ...
1
vote
2answers
39 views

Find distance between two poles.

2 poles, AB of length 2 metres and CD of length 20 metres are erected vertically with bases at B and D. The two poles are at a distance not less than twenty metres. It is observed that tan(angle(ACB)) ...
-2
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0answers
34 views

question asks when is the birthday??? [duplicate]

Question asks how to find out Cheryl's birthday??
2
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1answer
47 views

Unit square in a 2-sided square

Let ABCD be a square, |AB|=2. Let EFGH be a unit square included in ABCD (every point of EFGH is inside ABCD). If O is the center of ABCD, is it possible for O to stay outside EFGH?
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3answers
88 views

Weird Al revolution

Observe, Weird Al on a Thing; http://imgur.com/gallery/LBg2rYR I tried posting this as an image, but it's a .webm file. This motion is also found in coins or tires or other circular objects as they ...
1
vote
0answers
23 views

Tangent plane of a convex set.

Given a convex set $\Omega$ in $\mathbb{R}^n$ with smooth boundary, is $\Omega$ contained completely on one side of it's tangent plane at any point on the boundary? If so, how can we prove this? ...
1
vote
1answer
38 views

The approximate value of the angle in a right-angled triangle

If we have a right-angled triangle $c^2$=$a^2$+$b^2$ and if we assume $a<b$ and We have the formula $ \frac {180}{pi}\cdot\frac{(\frac43\cdot(2\cdot\sqrt{\frac{(c-b)\cdot ...
0
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0answers
26 views

Congruent Angles with Condition [on hold]

Let A be a point in the interior of triangle BCD such that $AB · CD = AD · BC$. Point P is the reflection of point A with respect to BD. Prove that $\angle PCB = \angle ACD$. I don't know how to ...
5
votes
2answers
122 views

Sierpinski (Triangle) for Other Polygons

The Sierpinski triangle can be "generated" by the algorihm where you start in the triangle, pick a vertex at random, then move half the distant towards it, draw a dot and then repeat this. I wasn't ...
2
votes
1answer
22 views

$2D$ plane geometry inequality

I am trying to shade a region on the $2D$ plane that can satisfy $$1-x-y \leq 0$$ What region would that be? Am I even drawing the line correct? thank you for any help.
0
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0answers
28 views

An orthogonal transformation with determinant 1 rotate $\mathbb{R^3}$ around an axis.

I'm studying differential geometry and need confirmation on the solution of the following problem. A rotation is an orthogonal transformation $C$ such that det $C=+1$. Prove that $C$ does, in fact, ...
1
vote
1answer
25 views

Need Assistance with Calculating the Area of a Square when given the diagonal.

It's been several years since I've done this stuff---I'm trying to brush up for a Praxis exam in a few weeks. I've come across a problem I'm having a lot of trouble with. I'm given a square. The ...
1
vote
1answer
51 views

A simple to explain solution to this kids' geometry puzzle

A smart 10 year old asked me basically this question. Consider a rectangle with both diagonals drawn in. Now ask if you can visit all the edges by travelling from some starting vertex and only ...
1
vote
1answer
41 views

How to find the focus of a parabola

To find the center of a circle, it's enough to choose three points on the circle and find the circumcenter of a triangle with those three points. When a parabola is drawn and the formula is not ...
2
votes
3answers
88 views

Proving $ \frac{1}{c} = \frac{1}{a} + \frac{1}{b}$ in a geometric context

Prove or disprove $$ \frac{1}{c} = \frac{1}{a} + \frac{1}{b}. $$ I have no idea where to start, but it must be a simple proof. Trivia. This fact was used for determination of resistance of two ...
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votes
1answer
21 views

Intersection between plane and circle

I have plane $$z = c$$ $$c - constant$$ and circle with center in $(0, 0, 0)$ and two points on circle $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$. How can I calculate coordinates of points of ...
3
votes
0answers
66 views

Laplace's equation in Polar coordinate, an example?

Consider Laplace's equation in Polar coordinate $ \frac {1}{r} \frac {\partial} {\partial r} (r \frac {\partial u} {\partial r}) + \frac {1} {r^2} \frac {\partial^2 u} {\partial \theta^2}$ with ...
2
votes
1answer
12 views

Identifying translations and rotations as compositions.

I am having trouble understanding the below which are the ones underline in red and blue. For the red: Why is that $R_{A,90}(A)=A$ and that $\tau_{AB}(A)=B$ As for the blue: Why is that ...
-4
votes
1answer
45 views

Circle sandwiched between two squares problem

Can anyone help with the problem attached? Many thanks in advance! Regards, P. This is what I've done so far a) The perimeter of square PQRS is 4 x 10 cm = 40 cm. The diagonal of square ABCD = ...
0
votes
2answers
14 views

Vector proof to show the line connecting two points on a triangle is parallel to a side.

If X and Y are points on sides AB and AC of triangle ABC, and $\frac{AX}{AB}=\frac{AY}{AC}$, the $XY||BC$. I'm supposed to prove this using vectors, but we haven't done too much of this yet, and I'm ...
1
vote
1answer
12 views

How can I find the inner limit of a line passing through a lune?

I have a crescent defined by two offset circles with different radii: a small one (let's call it outer circle) centered at (0,0) with radius ...
-5
votes
1answer
55 views

Geometry question, very tricky! Any help appreciated [on hold]

I have another one, sorry! Can you help with this one at all? Thanks! All four sides of a rhombus are equal. a Taking this as a starting point and using congruent triangles, prove that the opposite ...
6
votes
4answers
196 views

In a 30-60 right triangle the side opposite the 30 degree angle is half the length of the hypotenuse. Why? [on hold]

In a 30-60 right triangle the side opposite the 30 degree angle is half the length of the hypotenuse. A statement from the trigonometry section of Simmons' Precalculus in a nutshell. Please ...
2
votes
2answers
58 views

Volume of a parallelepiped, given 8 vertices

Given the eight vertices $(0,0,0)$, $(3,0,0)$, $(0,5,1)$, $(3,5,1)$, $(2,0,5)$, $(5,0,5)$, $(2,5,6)$, and $(5,5,6)$, find the volume of the parallelepiped. I'm having trouble finding the 1 vertex ...
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0answers
35 views

Proj of some ring.

Let $R= \mathbb C[x_1,x_2,x_3,x_4,x_5,y_1,y_2,y_3,y_4,y_5]$ be the polynomial ring and let $S$ be the subalgebra generated by $x_1x_2x_3x_4x_5, x_1x_2x_3x_4y_5, \cdots ,y_1y_2y_3y_4y_5$ (the ...
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votes
0answers
38 views

Why does this proof by bashing not work?

Given is a triangle $ABC$ with circumcenter $O$ and orthocenter $H$. The feet of the perpendiculars from $C$, $B$, and $A$ to the opposite sides are $F$, $E$, and $D$ respectively. Prove that ...
7
votes
4answers
361 views

How to construct a line with a given equal distance from 3 Points in 3 Dimensions?

Important: I'm now convinced that 4 points are needes in order to reduce the solutions to a finite number. (Which is necessary because I need ALL solutions) In a computer science context I need to ...
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0answers
20 views

angle between two lines on a sphere

What happen to the angle between two lines inscribed on a sphere of radius $1$ when its radius grows to $R>1$? My first thought is that it doesn't change at all..but i'm not sure, any suggestion ...
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0answers
23 views

Linear Operator in Euclidean Space

In oriented Euclidean space $E_3$ consider the following linear operator $$A(x) = x − a × (a × x)$$ where vector $a = e + 2f + 2g$. Here $\{e,f, g\}$ is an orthonormal basis in $E_3$ defining ...
0
votes
1answer
34 views

What is the height of this pyramid?

Let $W$ be the point in the base $(XYZ)$ of the pyramid such that $VW$ and $WZ$ are perpendicular. $XYZ$ is a right triangle and $XZ$ is perpendicular to $YZ$. What is the height of the pyramid? ...
-3
votes
1answer
83 views

Why a line is said to have infinite number of points? [duplicate]

Why a line is said to have infinite number of points? Is this so because a line is ever lasting or we can not count how many points does it have? Finite means: Having an end. Infinite means: No end! ...
3
votes
1answer
14 views

Let $R$ be any rotation and $P$ any reflection then $R \circ P$ and $P \circ R$ are both glide reflections

Let $R$ be any rotation and $P$ any reflection then $R \circ P$ and $P \circ R$ are both glide reflections I am having trouble showing $P \circ R$ is a glide reflection, I manage to get $R \circ P$, ...
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votes
1answer
21 views

sum of the squares of the reciprocals of the two parts of the focal chord of a parabola

Find the sum of the squares of the reciprocals of the two parts of the focal chord of a parabola. My attempt: Let $y^2=4ax$ be a parabola. Let PQ be the focal chord through the focus S$(a, 0)$ ...
2
votes
0answers
19 views

Proof: The inverse of the translation $T_{AB}$ is the translation $T_{BA}$

Prove: The inverse of the translation $T_{AB}$ is the translation $T_{BA}$ This is my work so far: Let P be any point of the plane and set: $P'=T_{AB} (P)$ We want to show ...
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0answers
17 views

Parallelogram with vertices 0, Xa, Xb, Xa+Xb (X is matrix, a and b are vectors)

There is a paralellogram with vertices 0, a, b, and a+b, whose area is $34$. What is the area of the parallelogram which has vertices 0, Xa, Xb, and Xa+ Xb, where X = \begin{pmatrix} 3 & -5 \\ -1 ...
6
votes
4answers
243 views

An ancient Japanese geometry problem.

NOTE: This very difficult problem of elementary geometry has an ancient Japanese source (See “Sacred Mathematics: Japanese Temple Geometry”. Princeton University Press, 2008, by F. Hidetoshi & ...
1
vote
1answer
24 views

Proof for diagonals of a rectangle

If a rectangle is a figure with four sides and four rectangular angles, I would like to prove that the diagonals are congruent and both meet in the midpoints. However, I don't know where to start this ...
0
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0answers
17 views

Unbounded Geodesics and Nonpositive Curvature

I have the following interesting(?) question: Let $M$ be a complete Riemann manifold. Suppose that it is of non-negative curvature. I want to know if $M$ has unbounded geodesics. As the question is ...
0
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1answer
34 views

Find length of oblique side of trapezium.

In a trapezium, the lengths of the two parallel sides are $6$ and $10$ units. If one of the oblique sides has length $1$ unit, then find the length of the other oblique side. Using the short parallel ...
0
votes
2answers
30 views

Trisecting a line in the complex plane

We have $x = 11-13i$ and $y = 35-i$. $a$ is a complex number which trisects the line segment joining $x$ and $y$. $a$ is also closer to $x$ than $y$. Find $a$. I'm not sure where to start. Would a ...
10
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0answers
83 views
+50

How prove this geometry inequality $R_1^4+R_2^4+R_3^4+R_4^4+R_5^4\geq {4\over 5\sin^2 108^\circ}S^2$

Zhautykov Olympiad 2015 problem 6 This links discuss olympiad problem none of student solve it,therefore, meaning this problem is so hard. Question: The area of a convex pentagon $ABCDE$ is $S$, ...
0
votes
1answer
19 views

Get angle in degrees of coordinate on circle.

So assume I have coordinates of two points on a circle, and the coordinate of the center of the circle. How would I go about finding the angle of the points in degrees?