Tagged Questions
3
votes
2answers
87 views
Euclidean Geometry Area Problem
Let $\Gamma $ be the circumcircle of triangle $ABC$. Let $A_0$ be the center of the circle lying outside of $\triangle ABC$ and which is tangent to the segment $BC$ and to rays $\overrightarrow{AB}$ ...
0
votes
0answers
40 views
Given 2 outer points of a perfect circle, find the centerpoint
Alright, I hope this makes some sense.
I am using a software that can create arcs.
This arc is defined by:
Begin point
End point
Center of "circle"
The center is supposed to be the center of the ...
12
votes
2answers
184 views
6 point lying on a common circle
$Z$ is an interior point of segment $XY$. Three semicircles are drawn over segments $XY$, $XZ$ and $ZY$ on the same side. The midpoints of the arcs are $M1$, $M2$ and $M3$ respectively. A circle ...
1
vote
1answer
54 views
Bounding box enclosing circles, that complies with ratio constraints
Given a circle centered at $A$, with radius $R_a$ and another radius $R_b$, I need to find a center for circle $B$ such that both circles are tangential, and the bounding box including both circles ...
10
votes
1answer
294 views
Proving collinear points
This problem is so hard that I cannot figure it out. I hope you guys can give me a small push on how to tackle this problem, as I have been thinking about this for, like a week. Here's the problem:
...
-4
votes
1answer
174 views
Geometric Definitions: What is a straight line? What is a circle?
What is a straight line? I need a geometric definition of it. The equation of a straight line is known to me.I am saying about a straight line of 2D plane.
What is a circle? I need a geometric ...
1
vote
2answers
95 views
area of a circle - 3/4th
How to find the pixels of that line which is crossing the circle?
Is there any formula?
Iam getting the line's end points
1
vote
1answer
175 views
Relationship between the sides of inscribed polygons
In my math textbook there's a demonstration for the calculus of the circumference of a circle that involves regular polygons inscribed in the circle, but I don't get it. The book gives the following ...
9
votes
4answers
266 views
Why do we use the Euclidean metric on $\mathbb{R}^2$?
On the train home, I thought I would try to prove $\pi$ is irrational. I needed a definition, so I used:
$\pi$ is the area of the unit circle.
But what is a circle?
A circle is the set of tuples ...
1
vote
1answer
83 views
Length bisection from circular arc
I am not sure if the following result is well known. I stumbled across it from the paper The Perimetric Bisection of Triangles by Dov Avishalom, where the result was stated without proof. I am ...
1
vote
2answers
55 views
rates of motion of projected points along a circle
Have I forgotten all my secondary-school geometry?
(That's not actually my question.)
Suppose $R>r>0$ and consider this circle
(later edit: I think $R>0$, $r>0$ is enough; we don't ...
4
votes
1answer
120 views
Why do derivatives of certain equations relating to circles yield other similar equations? [duplicate]
Possible Duplicate:
Why is the derivative of a circle's area its perimeter (and similarly for spheres)?
We all know that the volume of a sphere is:
$V = \frac{4}{3}\pi r^{3}$
and its ...
0
votes
1answer
667 views
Making a circle with paper folding, scissors, pencil, and a straightedge
Can we make a circle using paper folding, scissors, straightedge, anda pencil, allowing an infinite number of operations?
I think my chemistry teacher have show me once how to make it during the ...
8
votes
2answers
447 views
Sangaku: Show line segment is perpendicular to diameter of container circle
"From a 1803 Sangaku found in Gumma Prefecture. The base of an isosceles triangle sits on a diameter of the large circle. This diameter also bisects the circle on the left, which is inscribed so that ...
1
vote
2answers
361 views
How to calculate a specific area inside a circle?
I want to calculate the area displayed in yellow in the following picture:
The red square has an area of 1. For any given square, I'm looking for the simplest ...
5
votes
1answer
251 views
Is this concept of circle geometry known?
Astonishingly, no mathematician ever could give a "Mr. Foobar invented this"
whenever I came up with this construction, although it is very elementary.
Given are 3 circles C1,C2,C3 (avoid degenerate ...
3
votes
2answers
178 views
Circle bitangent angles
Say we have two circles $C_1$ and $C_2$ with radii $r_1$ and $r_2$, respectively. Let their centers be $d$ units apart. There are 4 bitangents, two outer and two inner.
Examine the intersection of an ...
2
votes
2answers
462 views
Area Between Three Circles of Differing Radii
From the link in wikipedia
http://web.gnowledge.org/wiki/index.php/Area_Between_Three_Circles_of_Differing_Radii
OPEN QUESTION:
What is the equation, in three variables, relating the radii of ...
5
votes
2answers
244 views
Finding point on a circle
I know how to find a point on a circle given a radius and an angle, but my knowledge of trigonometry doesn't extend much further than that. My question is probably best explained diagrammatically:
...
4
votes
2answers
275 views
name of a shape
Let P be a point, not the center, in the interior of a (round) disk D⊂ℝ² and let A and B be points on ∂D such that the line segments AP and BP have equal length. Choose an arc AB. What's the shape ...
6
votes
2answers
255 views
Two points on circle resulting in 5 equal regions
What values of $Z_1$ and $Z_2$ make the five regions of the unit circle, shown below, equal in area? $\overline{Z_1}$ and $\overline{Z_2}$ are conjugates of $Z_1$ and $Z_2$; in other words they lie ...
5
votes
3answers
728 views
How to determine arc measures from angles between secant and tangents (without trigonometry)
Given a circle, a point $H$ outside the circle, segments $\overline{HE}$ and $\overline{HT}$ tangent to the circle at $E$ and $T$, respectively, and points $I$ and $G$ on the circle such that $I$, ...
5
votes
3answers
7k views
Proof of Angle in a Semi-Circle is 90 degrees
There is a well known theorem often stated as the angle in a semi-circle being 90 degrees. To be more accurate, any triangle with one of its sides being a diameter and all vertices on the circle has ...
