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

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3
votes
3answers
166 views

Simple circle geometry/ similarity question

How would you prove that $a=b$ ? Would it be possible to solve this using similarity or trigonometry? Thank you in advance for any help. Any theorems or links would be appreciated.
2
votes
1answer
263 views

How to cut circle into $n$ parts (all cuts are parallel to each other) so that each chunk is the same area (i.e. $\pi r^2/n$)?

I have been working this problem for a few hours today, but I'm stuck. I started working on a case where $n = 3$: Let the radius of the circle be centered at $(0,0)$, with a radius $r$. The equation ...
0
votes
2answers
125 views

Circle-circle intersection on a spheroid

Does anybody have formulae to solve the following issue. If you have two circles, defined by their two centres, and a radius for each circle. Where (if the circles intersect) are the two points ...
0
votes
1answer
38 views

What are the applications? [duplicate]

How can I show that a sequence of regular polygons with n sides becomes more and more like a circle as n→∞? In which fields this concept is applied?
0
votes
1answer
74 views

what are the various fields in which circle is treated as infinite sided regular polygon?

What are the various fields in which circle is treated as infinite sided regular polygon? What I actually mean is , "can u suggest me some applications where circle is treated as infinite sided ...
0
votes
2answers
1k views

Circles in Complex Planes

Points on the circle centre C and radius r are given by the equation $|Z-C|=r$ or $(Z-C)(\overline{Z}-\overline{C})=r^2$. Where $Z = x + iy$. When multiplied out, I understand that we have ...
2
votes
3answers
423 views

A triangle has side lengths 4,6,8. A tangent is drawn to incircle parallel to side 4 cutting …

Problem : A triangle has side lengths $4,6,8$. A tangent is drawn to incircle parallel to side $4$ cutting other two sides at M and N, than length of MN is (a) $\frac{10}{9}$ (b) $\frac{20}{ 9}$ ...
2
votes
3answers
339 views

Geometry question involving a circle

If $P$ is a point inside a circle, how do you find the shortest distance from $P$ to the circumference of the circle?
2
votes
2answers
718 views

Circle Theorem - Alternate Segment Question

Hi there I have a maths question from my GCSE book which is just really bewildering me and my teacher. I have taken the maths question out from my book and made a computerized version and this is what ...
6
votes
0answers
225 views

What's the average distance between two discs in the plane?

Consider two discs in the plane of radius $r$ and $s$, with centers separated by a distance $l$. If we choose a point uniformly at random from each disc, what is the expected distance between the two ...
4
votes
2answers
172 views

How is the circle that fits beneath two adjacent circles related? [duplicate]

This is hard to search and probably easy to solve, but I keep finding articles about intersecting circles, and that is not what I'm after. I don't know what to tag this under, so if you know how to ...
1
vote
0answers
105 views

Optimization and derivatives homework

Find the dimensions of a right circular cylindrical can with both a top and a bottom that holds 8 cubic cm and is constructed with the least amount of material possible. Radius of can= cm Height ...
2
votes
1answer
31 views

Approximate sector between two lines?

I need to approximate a red figure. I know coordinates of three points (little transparent circles). I also know a count of segments I need to divide this figure. The angle may be from 0 to Pi and ...
3
votes
1answer
127 views

Triangles within square

Points E and F lie on the sides BC and CD of rectangle ABCD, the AEF is an equilateral triangle. point M is the midpoint of the AF. Prove that the triangle BCM is equilateral.
1
vote
3answers
819 views

Find the radius and centre of the circle $x^2 -6x +y^2 -2y -6=0$

Find the radius and centre of the circle $x^2 -6x +y^2 -2y -6=0$ Can someone please help me with this question? I'm quite lost with what I have to do.
0
votes
1answer
755 views

find the equation of the circle passing through the extremities of the diameter of the circle

find the equation of the circle passing through the extremities of the diameter of the circle $x^2 +y^2 +2x-4y-2=0$ $x^2 +y^2 =0$ $x^2 +y^2 -6x-8y-2=0$ I cant understand what the question asks ...
0
votes
1answer
147 views

find the equation to the circle circumscribing the quadrilateral formed by the straight lines

find the equation to the circle circumscribing the quadrilateral formed by the straight lines $$2x+3y=2$$ $$3x-2y=4$$ $$x+2y=3$$ $$2x-y=3$$ we can see that the first two and the last two are ...
3
votes
2answers
1k views

Prove using integration that $polygon → circle\space \text{as}\space number\space of\space sides → infinity$

Say we have a regular polygon $s$, with number of sides $n$: Is there a way to prove that as $n → ∞,\space $then $s → circle$ using integration?
1
vote
2answers
44 views

Find the equation of a circle.

If a circle which center is on the straight line $x-2y+3=0$ cuts both the x-axis and the y-axis, what is the equation of the circle? ANSWER: $x^2+y^2-6x-6y+9=0$ This is rather a straightforward ...
4
votes
2answers
124 views

Triangle and its circumcircle

Let $ABC$ be a triangle and $\Gamma$ its circumcircle. On sides $AC$, $BC$ lies respectively points $E$, $F$ such that $CE=BE$ and $CF=AF$. $CM$ is a median of triangle $EFC$. Show that line $CM$ pass ...
0
votes
1answer
568 views

Finding the condition for a straight line to be a tangent to a circle?

This is the question in my textbook-- Find the condition that the straight line $cx - by +b^2 = 0$ may touch the circle $x^2 + y^2 = ax + by $? My approach:- I made the distance of the center of ...
0
votes
1answer
51 views

Question about property of circle

We know that equal chords are equidistant from the center. However, I was curious if the lengths involved are proportional as well since the circle is a pretty symmetrical shape. Here's what I mean: ...
0
votes
5answers
346 views

Help in question related to locus of pair of tangent to a circle?

This the question in my text-book The tangent to $x^2 + y^2 = a^2$ having inclination $\alpha$ and $\beta$ intersect at $P$. If $cot\alpha$ + $cot\beta = 0$, then the locus of $P$ is : i really ...
8
votes
1answer
167 views

Is this curve the circumference of a circle?

Let $\Gamma$ be a single closed curve with no self-intersections on a plane which satisfies the following condition : Condition : For any distinct four points $P, Q, R, S$ on $\Gamma$, if the line ...
2
votes
1answer
105 views

Getting an angle

I have a unit circle, and two angles: $\alpha=\angle{JON}\in[0,\pi]$ and $\beta=\angle{IOM}\in[0,\frac{\pi}{2}]$. Using angles, we can get points $N$, $M$ as on the image. Then, dropping a ...
0
votes
0answers
43 views

Overlapping Circles Area [duplicate]

I have searched but could not find the exact question. Two circles with radii 5 intersect such that the center of one circle lies on the circumference of another. What is the area of the overlapping ...
1
vote
1answer
430 views

Finding the angle between 2 points on a circle

forgive me if this isn't the right place to ask this question but I am trying to figure out the value of theta along a line tangent to a circle from a starting position on the circle to an ending one ...
0
votes
1answer
55 views

Find a point given another point and angle

I have something starting at (50, 10) it then rotates counter clockwise by 30 degrees, around the point at (50, 0), essentially mapping out an arc of a circle. How do I find the point it now lies on?
1
vote
1answer
618 views

If inside a big circle , exactly n $(n \geq 3)$ small circles, each of radius r,can be drawn in such a way that each small circle touches t…

Problem : If inside a big circle , exactly n $(n \geq 3)$ small circles, each of radius r,can be drawn in such a way that each small circle touches the big circle and also touches its adjacent small ...
3
votes
1answer
92 views

Let P be a moving point such that if $PA$ and $PB$ are two tangents drawn from $P$ to the circle $x^2+y^2=1 ( $ A ,B being the points of contact) ,…

Problem : Let $P$ be a moving point such that if $PA$ and $PB$ are two tangents drawn from $P$ to the circle $x^2+y^2=1$ ( $A$, $B$ being the points of contact) , then $\angle AOB = 60^{\circ}$, ...
1
vote
3answers
796 views

Equation of a Circle from parametric functions of sin and cos

Given: x = 2 cos (t/2) y = 2 sin (t/2) How do we find the equation of the circle? I know that x^2 + y^2 = 1, where x = cos(t) y = sin(t) so x^2 = (2 cos (t/2))^2 y^2 = (2 sin (t/2))^2 How do ...
0
votes
1answer
55 views

Find the center of the circle… [closed]

Geometry | Circles | Equations of a Circle This is the equation for a circle: $$x^2 + y^2 + 4x + 2y - 11 = 0$$ Fill in the blanks for this answer box. Center: ( __ ,__ ) $$-$$ Radius: __
0
votes
1answer
325 views

Determine angle of incidence/reflection off of slanted line?

I'm working on an air hockey game (for learning purposes) and I'm currently struggling with some geometry. I'm trying to determine the new slope of the velocity of the puck when it collides with one ...
-2
votes
2answers
856 views

Find the equation of a tangent line at $(3,-1)$ on the circle $x^2+y^2+2x-y-17=o$ [closed]

Determine the equations of tangents from point $A( 3 , -1)$ to circle (C) of equation: $x^2+y^2+4x+8y+3=0$ Thanks in advance :)
1
vote
1answer
704 views

Intersection points of two circles.

I understand that this is a common question and typically I can solve them, but this one keeps messing me up: Find the points of intersection (A and B) on the circles $x^2+y^2+4x-10y+20=0$ and ...
0
votes
1answer
84 views

Finding Area and probability[ hard nut to crack].

Suppose that $X$ and $Y$ are iid uniform distribution with $U(0, 1)$ random variables. (a) What is $\mathbb P((X, Y ) ∈ [a, b]×[c, d])$ for $0 ≤ a ≤ b ≤ 1$ and $0 ≤ c ≤ d ≤ 1$ ? What is $\mathbb ...
4
votes
1answer
139 views

What does relative height to the hypothenuse means?

I have to solve the next problem: Given H (relative height to the hypotenuse) and R (radius of the circle inscribed in the triangle) of a rectangle triangle, can you calculate the value of its ...
0
votes
4answers
207 views

How do I find the center and radius of this circle? [closed]

How do I find the center and radius of this circle? $$4x^2+4y^2+24x-16y+41=0$$
1
vote
3answers
237 views

Define “y” value from the equation of circle

Let's take a circle. It has the following general equation to describe it: $(x-u)^2+(y-v)^2=r^2$ ,where $u,v$ is the coordinates of the center of the circle, and $r$ is the radius of the circle. If ...
0
votes
1answer
902 views

How do I find the equation of the line that passes through this circle?

Find the equation of the line that has x-intercept and passes through the center of the circle that has equation $$x^2 + y^2-4x+10y+26=0$$
0
votes
1answer
223 views

Inscribed Angles/ Central Angles

If $\angle ACB = 40^{\circ}$(see figure), and the area of the circle is $81\pi$, how long is the arc $ABC$? This is how i have approached this problem. First of all we know the area of cricle is ...
0
votes
3answers
251 views

How to determine the number of degrees overlap between two circular slices?

How do you determine the number of degrees that overlap between two circular slices like what is shown in the example below by the hatched area? EDIT: Note, the slices are orientated by a center ...
1
vote
1answer
3k views

How many circles of radius r fit in a single bigger circle of radius R?

Is there any formula to calculate how many circles of radius r fit in a single bigger circle of radius R? I'd apreciate if it didn't involve advanced math, like calculus (unless there is no other way, ...
0
votes
3answers
154 views

Finding the equation of a circle ?

My Approach: I know that the general equation of a circle is $x^2 + y^2 + 2gx + 2fy + c=0$. So, the aim is to fond the constants g,f,c.So, I should make equations relating these constants from the ...
-1
votes
1answer
184 views

Finding all points around a circumference of a circle

I'm trying to write a program that lets the user put in the center point of a circle and its radius, and the put in two points to form a rectangle. Then I'm wanting it to print out whether the if the ...
1
vote
2answers
136 views

Preimage of a function

The only way to get better at this sort of thing is to practice, and now I'm also trying to ask myself (and try to answer) more conceptual questions. If a circle with radius $r$ is given in ...
1
vote
2answers
1k views

area of shaded region in circle

Solution : $\angle O = \angle D = \theta$ (corresponding angles) Also we can use area of sector formula After that, I have no idea
3
votes
2answers
181 views

Questions on geometry of circles.

Triangle ABC is inscribed in a circle, and the bisectors of the angles meet the circumference at XYZ. Show that the angles of the triangle XYZ are respectively $90^\circ- A/2$, $90^\circ- B/2$, ...
1
vote
0answers
27 views

Best path for finding within a radius of x units from this point

Say i am standing at a point and knew there is one thing within a radius of x units from this point. What is best path to find that thing. Best can mean shortest, but the discussion can be more open. ...
2
votes
1answer
92 views

What am I doing wrong in this trigonometry/rate simulation problem?

I'm refreshing on some trig and cannot figure out how to solve this non-realistic word problem simulating a person walking in a circle. A person is located at the point (8,0) at time, t = 0, and ...