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
21 views

Stuck on a practice problem

The problem is as in the picture. Line AE is parallel to line DC and line BC is parallel to line DE. Find the area of the pentagon. Here is what I am stuck on about this problem. I managed to draw ...
4
votes
2answers
126 views
+50

Maximum square cells in a rectangle

I know this sounds like bin packing but it's a bit different so please read the question to the end. Given a rectangle of known width and height, I need to divide it into smaller rectangles using ...
4
votes
0answers
14 views

Random 3D points uniformly distributed on an ellipse shaped window of a sphere

I know how to generate random points uniformly distributed on the surface of a sphere: ...
0
votes
0answers
8 views

Prove that every set of n points in R3 with diameter L can be covered by a cube with side length L.

Prove that every set of n points in R^3(3 dimension) with diameter L can be covered by a cube with side length L. Can someone show me the picture of draw it? I can't figure it out in picture.
-1
votes
0answers
27 views

Trigonometry problem - No right angles triangle [on hold]

I got a trigo problem I need to solve asap :p I've got a triangle, with no right angle. 1 of the side length is know, and the opposite angle is known too. I am spliting the triangle with a line ...
-1
votes
0answers
15 views

Prove that P∪Q is convex if and onl if every interval [v,w] ⊂ P∪Q for all vertices v of P and w of Q. [on hold]

This is geometry Problem. How do I start to prove this problem? Let P, Q ⊂ Rd (d= 2) be two convex polytopes. Prove that P∪Q is convex if and onl if every interval [v,w] ⊂ P ∪ Q for all vertices v ...
-3
votes
0answers
21 views

Show that the probability that O is in (x1, x2, x3) is equal to ¼. [on hold]

This is Geometry problem. I don't know where the number 1/4 came from and how to prove this problme.. Suppose points x1, x2, and x3 are chosen uniformly and independently at random from the unit ...
0
votes
1answer
6 views

Intersection of two equally long lines in a set with diameter $1$

Let $A := \{x,y,z,w\} \subset \mathbb R^2$ be a set with diameter less or equal to $1$. Let $L(x,y)$ and $L(z,w)$ be the linesegments between the points $x,y$ resp. $z,w$. If both lines have length ...
0
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0answers
11 views

Constructing triangle using side length-median relationship

$m^2_a=\frac{2b^2+2c^2−a^2}4$ $m^2_b=\frac{2c^2+2a^2−b^2}4$ $m^2_c=\frac{2a^2+2b^2−c^2}4$ Solving for a,b,c in terms of $m^2_a,m^2_b,m^2_c$ gives: $a^2=\frac{8m^2_b+8m^2_c−4m^2_a}9$ ...
0
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0answers
13 views

Finding an ellipsoid equation using its projected views

I want to find 3D equation of a falling droplet that I have considered it as an ellipsoid. I put two cameras, one in xy plane and another in zy plane to capture two projected views of the droplet and ...
2
votes
0answers
37 views

Smallest area of polygon with $n$ sides all of length $1$

Given an odd number $n$, consider all non-self-intersecting polygons with $n$ sides, all of length $1$. What is the infimum of their areas? We can approach $\sqrt 3/4$ by approximating an equilateral ...
2
votes
1answer
26 views

Find the equation of line and finding a point in given example

The outer circle is $x^2+y^2=1$ and the smaller circle is $x^2+(y+1-r)^2=r^2$. The arclength is parameterised anticlockwise with $s=0$ at the bottom as shown. If we know $s_n$ and $s_{n+1}$ can we ...
3
votes
1answer
53 views

Area of square reduced to circle.

There is a method to calculate area of a circle by inscribing the circle into a square and filling the edges outside the circle with squares. The area of the circle will be area of square minus area ...
1
vote
1answer
24 views

Relationship between the altitude of an isosceles triangle and segments drawn to the lateral side from a point on the base.

Question :In an isosceles triangle, the sum of the distances from each point of the base to the lateral sides is constant. I've tried a couple of things, but it seems like this statement is not true. ...
2
votes
1answer
23 views

Volume of a sphere “corner”

I would like to find the formula of the volume of the "corner" of a sphere of radius R, more specifically the volume delimited in a sphere by the intersection of two perpendicular planes, one parallel ...
0
votes
0answers
29 views

How to find the components of a vector, given magnitude and angle?

Problem The velocity of an aeroplane is $100$ km/h at an angle $30$ degree from north toward west. Draw a vector diagram to obtain its north and east components. Progress The work I already tried ...
1
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2answers
24 views

Description of real projective spaces in various contexts

What I want to know is : What is the description of real projective spaces (specially $RP^0$, $RP^1$, $RP^2$) respectively in context of topology, geometry and algebra? I'm searching for simple ...
0
votes
2answers
27 views

External angle bisectors of a triangle

Exterior angle bisectors of the side $\triangle ABC$ at vertices $B$ and $C$ intersect at $D$. Find $\angle BDC$ if $\angle BAC=40^{\circ}$ I cannot visualize this problem... If I draw a triangle and ...
1
vote
0answers
23 views

linear algebra question

Consider $n$ convex polytopes $S_1, \cdots, S_n$ and a set of matrices $W$ such that each matrix $A\in W$, we have that the $i$-th row of $A$ is a member of $S_i$. (In general $W$ is infinite.) ...
0
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0answers
19 views

Identify regions in 3D space and assign a point to a region

Sorry if the question is duplicated, I don't even know what to search for solve this problem. I have for example 10 planes with their equation: Ax + By + Cz = D and a list of 3D points. Those plane ...
2
votes
0answers
176 views

Maximum Area of rectangle without any monsters

Given a rectangular grid of N*M (1-based indexing) in which their are k monsters on k different cells.Now we need to answer Q queries in which we will be given lowest row number(L) and highest row ...
1
vote
1answer
273 views

Geometry Problem and Isosceles Triangle

$ABC$ is an isosceles triangle with $AB=AC$, $\angle BAC=96^\circ$. $D$ is a point such that $\angle DCA=48^\circ$, $AD=BC$ and angle $DAC$ is obtuse. What is the measure (in degrees) of $\angle DAC$? ...
3
votes
2answers
30 views

Circle rotating within a circle (roulette)

This was something in a course of mine I'm a bit too thick to see. If one takes a circle of radius $3$ and a circle of radius $1$, and rolls the smaller circle smoothly inside the larger one until the ...
0
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0answers
25 views

How to determine two functions having similar shape without drawing [on hold]

is there a measure or method to determine two functions having similar shape without drawing the similar means that they have similar structure after plot3d when doing 3d object recognization is ...
-4
votes
1answer
40 views

Volume of water [on hold]

Please Calculate volume of water in a sphere container with radius r that is filled with water up to the height h.
3
votes
0answers
33 views

Notion of a distribution as acting on tangent spaces

I'm reading a paper that uses distributions in a way I'm not entirely comfortable with. To be precise, I'm not sure what definitions the author is working with and can't find any natural way to fill ...
2
votes
0answers
83 views
+50

What is the smallest possible angle of this polygon?

A convex polygon contains a square with side-length 1 and is contained in a parallel square with side-length 2 (which is its smallest containing square). What is the smallest possible angle of the ...
3
votes
1answer
29 views

Longest chord inside the intersection area of three circles

I am currently working on my masters thesis in computer science and I stumbled onto a geometry problem. My goal is to compute the length of the longest possible chord inside the intersection area of ...
2
votes
0answers
24 views

Does the distance between points determine the shape?

Given three pairwise distances between three unknown points in a plane, the positions of the triangle vertices are uniquely determined up to a rotation and translation. Is this true for an arbitrary ...
0
votes
0answers
17 views

Finding Minimum Distance of a Point from Curve

While finding the distance of a point from a curve (which is graph of a function), the usual method I saw is as follows: given a point and a curve $\{x,f(x)\}\colon c\in\mathbb{R}$ (where ...
0
votes
1answer
19 views

Angle of three independently chosen points on a cricle

If a,b,c are three points on a circle (viewed in $\mathbb{R}^2$ not disc) chosen independently and uniformly,and p(x) is the probability that at least one of the angles of the triangle formed by the ...
1
vote
2answers
32 views

Distance of a Point from Hyperbola

Consider the part of hyperbola $H_{+}=\{(x,1/x)\colon x>0\}$ in the first quadrant, and $(a,b)$ any point in the plane (for sake of convenience, say $a,b>0$). If $(a,b)$ does not lie on the ...
2
votes
1answer
27 views

Prove that secants of a circle pass through a common point

Let $A$, $B$, $C$, $D$, and $E$ be five points on a circle. For any three points, we draw the line going through the centroid of the triangle formed by these three points that is perpendicular to the ...
1
vote
1answer
643 views

Find the Closest and Farthest Points of a Cube

This has to do with collision detection between a ray and a cube. I have a camera position that I am looking from and a ray is being shot into the scene which contains a cube. I have the ray ...
0
votes
1answer
29 views

Prove concurrency (probably using Carnot's Theorem)

Let $ABC$ be a triangle. An arbitrary circle $(K_a)$ passing through $B, C$ intersects $CA, AB$ again at $A_b, A_c$, respectively. Define $B_c, B_a, C_a, C_b$ similarly. Prove that the perpendicular ...
0
votes
1answer
32 views

Rotation about a point other than the origin

It is challenging for me to see the rotation of image ABCD to get to Aprime,Bprime,Cprime,Dprime. It is easy to see the translation of the prime figure to the double prime, but not so much the ...
-1
votes
1answer
17 views

How do I Solve this Coordinate Geometry Word Problem? [on hold]

I need help with this question: The coordinates of the end points of a line segment $PQ$ are $P(3,7)$ and $Q(11,-6)$. Find the coordinates of point $R$ on the y-axis such that $PR = QR$.
2
votes
1answer
27 views

Vectors and polyhedra: a surprising fact

Given a $n$-faced polyhedron, associate to each face an outward-pointing normal vector with length equal to the area of that face. Show that the sum of these $n$ vectors is zero. I've already proved ...
1
vote
1answer
27 views

Induction proof of the area of a square

English is not my first language, so I'm sorry if I'm not very clear. I can clarify any question you have. Also, I don't know how to use that math formatting so I apologize for it. So I was asked to ...
3
votes
7answers
2k views

The perimeter of the rectangle is $20$, diagonal is $8$ and side is $x$. Show that $x^2-10x+18=0$

My friends recently took a Maths GCSE. In the paper, they came across a very difficult question which we spent a full half-hour train journey trying to figure out. We didn't manage it, so I've come ...
0
votes
1answer
43 views

Two circles are tangent to each other, find the ratio of line that splits the area into $1:2$

There is one circle with radius $1$. There is another circle with radius $2$. They are tangent to each other and touch each other at point $c$. A line through $c$ splits the area formed by the ...
1
vote
2answers
27 views

Relation of length of a projection of a point to a line

In the given figure, can it be said that $x \leq a + b - d$?
0
votes
0answers
17 views

Finding locus problem

Let a given line $L_1$ intersect the $x$- and $y$ axis at $P$ and $Q$ respectively. Let another line $L_2$ perpendicular to $L_1$, cut the $x$ and $y$ axis at $R$ and $S$ respectively. Show that the ...
2
votes
0answers
20 views

Find mirror image of an point

I have a homework assignment that I have solved but don't know if its correct. The assignment is to find the mirror image of the point $(3,4)$ on the line $y = 2x + 1$. I call the mirror image Q(a,b) ...
1
vote
1answer
17 views

Assuming a ray defined by a starting point and a direction. How can I tell if a plane is behind it or in front of it?

If I have a ray defined by a starting point and a direction, and a plane defined by its normal and its distance from the origin, how can I tell if the plane is in front versus behind the ray? By ...
5
votes
3answers
138 views
+250

Pentagon Geometry

$ABCDG$ is a pentagon, such that $\overline{AB} \parallel \overline{GD}$ and $\overline{AB}=2\overline{GD}$. Also, $\overline{AG} \parallel \overline{BC}$ and $\overline{AG}=3\overline{BC}$. ...
1
vote
1answer
16 views

How to work out the equation for surface to volume ratio?

I want to work out the equation for volume of half a sphere against the surface area of the circle at the widest part of the sphere. The equation of the half sphere is (2/3) * (pi * r ^3), where r is ...
1
vote
2answers
4k views

2D - Coordinates of a point along a line, based on d and m - Where am I messing up?

LATER EDIT: I managed to find the errors in my equations below. It was a sign mistake on one of the terms (- instead of +). Having corrected that, the method which I describe below WORKS, but DON'T ...
0
votes
1answer
27 views

Viviani on Sphere parametrization

How should parametrization of the 2 parameter surface of a sphere (latitude u, longitude v) be changed to result in 1 parameter curve of Viviani?
0
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0answers
20 views

“Circle” on pseudosphere

How should parametrization of the 2 parameter surface of a pseudosphere ("latitude" u, longitude v) change to result in a 1 parameter curve of constant geodesic curvature?