Questions on the circle, a curve composed of points that are at a fixed distance from a fixed point.

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2
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1answer
18 views

Interior Angle Embedded in a Triangle Embedded in a Circle

With only knowing the angles of $B$, $C$, and $D$ (shown above), is it possible to find the interior angle $A$? And if so, how?
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1answer
30 views

Area of rectangle?

A circle touches two adjacent sides of a rectangle AB and AD at points P and Q respectively. Third vertex C of the rectangle lies on the circle. The length of perpendicular from vertex C to he chord ...
-3
votes
1answer
61 views

What radius circle to remove from unit circle to make golden earring?

A circular lamina of radius $x$ is removed from a circular lamina of radius $1$. If the center of gravity is at the edge of the smaller circle (along the line connecting the two centers) what is $x$? ...
3
votes
3answers
44 views

The equation of a tangent to a circle at a given point

18. Show that the equation of the tangent $PT$ at the point $P \left(\frac{1}{5}, \frac{3}{5}\right)$ on the circle $$x^{2} + y^{2} + 8x + 10y - 8 = 0$$ is $3x + 4y - 3 = 0$. Find ...
0
votes
1answer
659 views

Geometry Find the Radius of a circumcircle given the area of the triangle

Ok so here is what I know, the circumcircle of an equilateral triangle with an area of $4\sqrt{3}$ is drawn, calculate the radius lenght of the circumcircle. I also know that to find the radius I ...
-1
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0answers
16 views

Finding equation of tangent to circle which is also parallel to the given line.

I want to find out the equation of tangents to the circle x^2+y^2+2gx+2fy+c=0 which are parallel to the line y=mx+k. Is it correct if I assume the equation of the tangents to be y=mx+q1 and y=mx+q2 ...
0
votes
0answers
24 views

To draw a perpendicular on the diameter AB of a circle from an external point P using only a straight-edge.

A perpendicular is to be dropped from external point P on diameter AB I know this question is a duplicate of potato's post, but in potatos post altitudes of triangles were used. But a property of ...
2
votes
2answers
30 views

Proving a differential equation is a circle

So, I have solved the differential equation, to find the general solution of: $$\frac{y^2}{2} = 2x - \frac{x^2}{2} + c$$ I am told that is passes through the point $(4,2)$. Using this information, ...
3
votes
2answers
33 views

How to find the equation of diameter of a circle that passes through the origin?

So this was a question that I was solving that got me stuck. Its as follows: Q. Find equation of diameter of the circle $x^2 + y^2 - 6x + 2y = 0$ which passes through the origin. Now I have tried the ...
-2
votes
0answers
39 views

circle-shaped wave [on hold]

$y = \sqrt{1 - (x - 2) ^ 2}$ $y = -\sqrt{1 - x^2}$ I generated a partial wave with those 2 equations, basically chopping off the top of a circle and shifting it to the right. Is there a single ...
8
votes
6answers
471 views

Finding the largest triangle inscribed in the unit circle

Among all triangles inscribed in the unit circle, how can the one with the largest area be found?
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0answers
21 views

Write a detailed Proof: The diameter of a circle subtends a right angle at the circumference. [duplicate]

Write a detailed Proof: The diameter of a circle subtends a right angle at the circumference. I am stuck, can you please help.
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votes
3answers
44 views

Proof concerning circles

How do I prove that the diameter of a circle subtends a right angle at a circumference? Thank you in advance! I haven't got the slightest idea.
1
vote
1answer
31 views

$y^2 = |\cos(\pi*x/2)|$ generates an infinite number of adjacent circles on the line $y = 0$.

http://www.wolframalpha.com/input/?i=y%5E2+%3D+%7Ccos%28pi*x%2F2%29%7C The generation for the infinite string of circles on $y = 0$. Is there a relation that generates an infinite number of square ...
1
vote
0answers
34 views

Intersecting lines in sectors of a circle.

Good day everyone, I'm trying to simulate a Laser Range Finder (LRF for short) in a corridor environment. I'm including a small fast sketch I did of this. I can't upload images yet, so I include just ...
5
votes
3answers
72 views

Given two points, how to find a circle through them that's also tangent to the $x$-axis?

A seemingly simple geometry problem that is surprisingly difficult. I want to find the radius of a circle that is tangent to the $x$-axis, but also must contain two given points. I understand there ...
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votes
0answers
27 views

Prove that ABCD is cyclic if and only if it is a rectangle [closed]

Prove that $ABCD$ is cyclic if and only if it is a rectangle, in which case its circumcenter is the point where its diagonals intersects.
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votes
1answer
34 views

How do you express the following equations for a circle? [closed]

A circle of radius a is centered at a point r1. (a) Write out the algebraic equation for the circle. (b) Write out a vector equation for the same circle. (c) How would you modify (a) and (b) above ...
4
votes
4answers
6k views

Relation between chords length and radius of circle

Two chords of a circle, of lengths $2a$ and $2b$ are mutually perpendicular. If the distance of the point at which the chords intersect,from the centre of the circle is $c$($c<$radius of the ...
1
vote
2answers
28 views

Average distance from center of circle to evenly-distributed points within it

With some number of points that are evenly/uniformly (assuming those mean the same thing) distributed within a circle of radius 1, what is the average distance from the center of the circle to a ...
11
votes
6answers
17k views

Area of intersection between two circles

Suppose you have 2 circles that intersect each other in such a way that each circle passes through the other's center. What is the area between the circle(or common area) i.e. area between the centres ...
0
votes
1answer
347 views

Calculus Riemann sums for circle and ellipse

I ran into this problem today. I need to compare the Riemann sums for a circle and an ellipse. I have no idea as where to start. Here's the question:
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votes
4answers
70 views

Find Perimeter of shaded region in semicircle. [closed]

What is the Perimeter of shaded region in semicircle if four small semicircles have radii of 1,2,3,4 respectively? a. 10 $\pi$ b. 20 $\pi$ c. 40 $\pi$ d. 60 $\pi$
2
votes
2answers
47 views

Find the length of tangent $x$.

Two circles $C_1$ and $C_2$ of radius $2$ and $3$ respectively touch each other as shown in the figure .If $AD$ and $BD$ are tangents then the length of $BD$ is $a.)3\sqrt6\\ b.)5\sqrt6\\ ...
4
votes
4answers
124 views

What is the area of shaded region which is lies between outer and inner circle.

There is a outer circle with radius 2r and another inner circle with radius r whose center is the middle of big circle.As depicted in the following figure. Foo graph Image There is a sector of 120 ...
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vote
3answers
61 views

Find the area of the region $ABCD$.

In the Figure $\square PQRS$ is a square with side $2\sqrt6$. By joining the midpoints another square $\square WXYZ$ is formed . Circles are drawn with $4$ vertices as the center and radius equal ...
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vote
4answers
42 views

A line through the point P(8, -7) is a tangent to the circle C at the point T. Find T

Circle C equation $(x+5)^2+(y-9)^2=25$ A line through the point P(8, -7) is a tangent to the circle C at the point T. Find T. I tried simultaneous equations: 1. $(x+5)^2+(y-9)^2=25$ 2. $y = ...
0
votes
2answers
307 views

Diameters and Circles

I have a question (given by a teacher) that looks really easy but then when I thought about it, couldn't find a way to find the answer. It is a proof question relating to diameters: Prove that any ...
1
vote
4answers
40 views

A line through the point P(8, -7) is a tangent to the circle C at the point T. Find the length of PT.

Circle C equation $(x+5)^2+(y-9)^2=25$ A line through the point P(8, -7) is a tangent to the circle C at the point T. Find the length of PT. The question itself is easy when using pythagoras, ...
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votes
3answers
40 views

How do you find the intersection(s) of two circles with equal radii? [duplicate]

I have two circles with the following equations: \begin{equation*} (x-a_1)^2+(y-b_1)^2=r^2 \\ (x-a_2)^2+(y-b_2)^2=r^2 \end{equation*} The two radii are equal. How do you find the intersections of any ...
6
votes
1answer
528 views

Relationship between two centers of circles in a Venn diagram

Let $S$ be a circle of 1 unit area. No part of circles $A$ and $B$ are outside the circle $S$. Let $n(S)=1$, $n(A)$, and $n(B)$ be the area of circle $S$, $A$, and $B$, respectively. For the given ...
1
vote
2answers
35 views

Help for a problem with inscribed triangles

If we have a triangle $ABC$ with $AB = 3\sqrt 7$, $AC = 3$, $\angle{ACB} = \pi/3$, $CL$ is the bisector of angle $ACB$, $CL$ lies on line $CD$ and $D$ is a point of the circumcircle of triangle $ABC$, ...
26
votes
13answers
28k views

Calculus proof for the area of a circle

I was looking for proofs using Calculus for the area of a circle and come across this one $$\int 2 \pi r \, dr = 2\pi \frac {r^2}{2} = \pi r^2$$ and it struck me as being particularly easy. The only ...
0
votes
0answers
31 views

Find the distance between the centre of a circle and a bisector using linear algebra.

I am trying to work out the distance (D) in the above diagram. I know the points A - C. My first approach was to try the following: Create a line equation for the green line using A and B. ...
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vote
2answers
361 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 ...
0
votes
2answers
41 views

Find centre of circle with equation of tangent given

(4,1) is a point on one end of the diameter of a circle and the tangent through the other end of the diameter has equation 3 x- y=1. Determine the coordinates of the center of circle. What got me ...
0
votes
1answer
55 views

How to evaluate solid angle subtended by a segmented circle?

The diagram above shows a circular plane, centered at the origin 'O', has a radius $7 cm$. Two identical rectangular strips, each having width $2 cm$, are thoroughly cut off from the circular plane ...
1
vote
1answer
301 views

Inner tangent between two circles formula

As a programmer I need to draw the inner tangents between two circles, but only the segments, not the whole line. But the internet is surprisingly hostile to lazy programmers who don't know their ...
167
votes
27answers
29k views

Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers

An exam for high school students had the following problem: Let the point $E$ be the midpoint of the line segment $AD$ on the square $ABCD$. Then let a circle be determined by the points $E$, $B$ and ...
1
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1answer
28 views

Proving and deriving equation of a circle

Attached below is the past examination question. I'll be presenting my thoughts and queries on it. I initially thought of breaking this entire challenge down into multiple smaller ones. Prove ...
3
votes
3answers
101 views

Twelve identical circles touching one another on the surface of a sphere

Twelve identical circles are to be drawn on a spherical surface having a radius $R$ such that the circles touch one another at 30 different points i.e. each of 12 circles exactly touches other five ...
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votes
2answers
47 views

How to integrate this integral using Cauchy? [closed]

How can i find Solution use Cauchy Integrate? \begin{align*} \int_{|z-1|=1}\frac{1}{z^3-1}dz \end{align*}
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0answers
32 views

Calculate radius and angle of circle connecting two vectors

I have two vectors that lie on a circle. How do I calculate the radius of the circle and the angle between the two lines from the center of the circle to the two vectors?
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votes
0answers
21 views

Calculate new pitch and roll after rotating about the z axis

I am wanting to know how to find out the new pitch and roll values when rotating around a circle. I have become a little stuck on how to achieve this, but hopefully someone will be able to point me in ...
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vote
2answers
31 views

Deriving an equation for acceleration in circular motion

I have a question: A particle starts to move from rest in a circle of radius 3m, so after $t$ seconds its speed is $5t+1$m/s. Find its acceleration after 1 second. I have tried differentiating ...
0
votes
0answers
43 views

Ulam Spiral, what angle does x fall on?

Morning all, I'm trying to work out what angle a given number will fall on within the Ulam Spiral. The formula I have so far is this: $$ \dfrac{180 \times\sqrt{x}-255}{360} $$ For example using $x= ...
1
vote
1answer
22 views

Parametric equation of clock hands

I am trying to draw a clock with both hour and minute hands in a computer program. The movement of the clock hands would mirror a traditional wall clock (hours from $12, 1, 2, 3,..., 11$ and back to ...
0
votes
2answers
22 views

Finding the points of intersection on a circle

Before addressing my issues, below is the question from a past examination paper along with a diagram I dre in order to facilitate readers. 3(a) A circle has center $C(5, 8)$ and radius ...
4
votes
2answers
592 views

Prove that the centre of the nine-point circle lies on the midpoint of the Euler line

In $\Delta ABC$, $AD, BE, CF$ are the altitudes and $\Delta A'B'C'$ is the medial triangle. $K, L, M$ are the midpoints of $AH, CH, BH$. Consider the nine-point circle with centre $G$ (not to be ...
5
votes
2answers
212 views

Competition style problem circa 1992

We're given a triangle $ABC$. Going clockwise, let $B_1$ and $B_2$ be distinct points on the segment $AC$ ($B_1$ is between $A$ and $B_2$), let $A_1$ and $A_2$ be distinct points on the segment $CB$ ...