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

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1answer
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How do you express the following equations for a circle?

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 ...
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2answers
26 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 ...
2
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2answers
43 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\\ ...
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4answers
50 views

Find Perimeter of shaded region in semicircle. [on hold]

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 $\pi$
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4answers
41 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 = ...
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3answers
57 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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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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3answers
38 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 ...
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2answers
34 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 $ABC$, ...
4
votes
4answers
114 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 ...
0
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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. ...
0
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2answers
38 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 ...
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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 ...
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0answers
29 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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2answers
45 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*}
2
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0answers
16 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 ...
3
votes
3answers
98 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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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 ...
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0answers
42 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= ...
0
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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 ...
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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 ...
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0answers
20 views

Geometry packet with inscribed shapes and areas of shaded regions [closed]

I have a math problem that has a cross inscribed inside of a circle. The circle parts are shaded and inside the cross there is the number 2. It says to find the area of the shaded region but I have no ...
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2answers
52 views

Let $y=x^2+ax+b$ cuts the coordinate axes at three distinct points. Show that the circle passing through these 3 points also passes through $(0,1)$.

Let $y=x^2+ax+b$ be a parabola that cuts the coordinate axes at three distinct points. Show that the circle passing through these three points also passes through $(0,1)$. Since, the graph of the ...
2
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1answer
43 views

Proof about the coordinates of the centre of a circle which touches another circle and the $y$-axis

Question 16 goes as follows: 16. Given that the circle $$x^{2} + y^{2} + 2gx + 2fy + c = 0$$ touches the $y$-axis, prove that $f^{2} = c$. A circle, with its centre in the first ...
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1answer
25 views

Geometry: Perimeter of triangle formed by intersections of tangents

I'm a bit stuck on the question below, and I wondered if anyone out here might be able to help: Construct a circle with a centre in O(0,0) and a radius of 5. Two tangents of the circle intersect in ...
4
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2answers
26 views

Help setting out a proof about the circle $x^{2} + y^{2} + 2gx + 2fy + c = 0$

16. Given that the circle $$x^{2} + y^{2} + 2gx + 2fy + c = 0$$ touches the $y$-axis, prove that $f^{2} = c$. So, because the circle touches the $y$-axis, we know that there is a ...
6
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1answer
77 views

How to divide a pizza between friends equally without using centre

Here's a really fun question a friend told me abut. He claims to know the correct answer, and told me the answer, but left proving the answer as an exercise to me. Now, It's been ages since he asked ...
0
votes
1answer
14 views

Finding the radius of excircles from a right angled triangle

Right angled triangles have 3 excircles, I'm struggling to find a formula which gives me the radius of all three excircles, I've been struggling with this for a while. I've done some googling and I ...
0
votes
1answer
19 views

Find the tangents to circle

Let $ \Gamma : x^{2} + y^{2} - 6x - 4y + 8 = 0 $ be a circle. Find the equations of the tangents to $ \Gamma $ which pass through $ D(8, 7) $.
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0answers
36 views

Calculate parametric bounds of a circle in a 2D quadrilateral

Given a 2D quadrilateral defined by the points $(p0, p1, p2, p3)$ and a circle centered at $c$ with a radius of $r$, I want to find a quad in the parametric space of the outer quad that tightly bounds ...
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3answers
62 views

How to find the rules for a circle? [closed]

I am having issues with the questions below. If you would be able to give me an worked example, that would be appreciated! In the diagram, $A$ and $B$ are points on the circumference of a ...
2
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0answers
44 views

Triangle side-length problem

my problem is the following. A triangle ABC is given. P is a point on $\overline{AB}$. $k_1, k_2, k$ are the radii of the in-circles of APC, BPC, ABC. $s_1, s_2, s$ are radii of the ex-circles of ...
0
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1answer
55 views

Trapezoid and isosceles triangle

I have got a problem which I have to solve for my practive for an exam. Hope you can help me. An isosceles trapezoid $ABCD$ with the parallel sides $\overline{AB}$ and $\overline{CD}$ is given. ...
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2answers
26 views

How to the Find the Radius of a Sector

I know how you find out the Area of a Sector and the Arc Length but I'm not sure how to find out the radius of a circle? I understand that there are formulas but I find them quite confusing... ...
2
votes
1answer
25 views

Convex quadrangles

there is a quadrangles ABCD with $|AB| + |BC| = |AD| + |DC|$. The beam $AB$ cuts the beam $DC$ in the point $X$. The beam $AD$ cuts the beam $BC$ in the point $Y$. Now show that \begin{equation*} ...
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vote
1answer
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A Circle Problem

A circle $K$, a tangent $T$ and a point $A$ on $t$ are given. Find the locus of all point $X$ for which points $Y$ and $Z$ on $T$ exist which are equidistant from $A$ and make $K$ the incircle of the ...
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1answer
23 views

Projective transformation a parabola to a circle

Take the parabola $x^2 - y = 0$ in the cartesian plane. I'm not entirely sure about this, but we can express this using homogenous coordinates as $X^2 - Y = 0$ (the $W$ coefficient is $0$?) With the ...
0
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1answer
48 views

To what extend a polygon can be considered a circle?

I have a polygon of which I know: Area $x_{\max}$, $x_{\min}$ $y_{\max}$, $y_{\min}$ and I would like to establish to what extend the polygon can be considered a circle. From what I found, for ...
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0answers
27 views

Prove special case of Brianchon's theorem using inversion

Brianchon's theorem says: When a hexagon is circumscribed around a conic section, its principal diagonals (those connecting opposite vertices) meet in a single point. From interactive demo: ...
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2answers
29 views

Find the radius of a circle given a known smaller circle and other information.

There is a large circle with two smaller circles on the inside edge (each $r=6$), the distance between each circle being $50$ (that is directly not along the curvature of the outer circle) and the ...
0
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1answer
16 views

Find correleation between values and degrees

I have an arc that starts at $252$ degrees and ends at $288$ degrees, I would like to assign non - linear values on it with this ratio: $1 - 180$ degrees. $5 - 135$ degrees. $10 - 90$ degrees. $30 - ...
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1answer
18 views

difference between normal and diameter in circle.

A line through the centre of the circle meet the circle at two points is called a)normal b)tangent c)secant d)diameter I am pretty sure that the answer is diameter but my notes say the answer is ...
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2answers
29 views

Move a point with known angle on a circle

Having a circle of radius $R$ with the center in $O(0, 0)$, a starting point on the circle (e.g. $(0, R)$) and an angle $\alpha$, how can I move the point on the circle with $\alpha$ degrees? I need ...
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2answers
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How to calculate angles and areas (circles)- AS Maths

Hi here's the question: A(-1,-4) and B(6,-5) are points on the circumference of a circle, centre D(3,-1). The tangents at A and B intersect at C. How would I find the angle ACB and the area of ACBD? ...
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1answer
49 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 ...
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0answers
20 views

Check if points are sorted in circular order

How do you check if points are sorted in circular order (regardless of clockwise or counter-) (assuming they don't exactly form one whole circle, what matters is the points are sorted in a circular ...
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0answers
33 views

Truth value of a mathematical statement about circles?

Let $A$ be the set of circles in the plane with center $(0,0)$ and let $B$ be the set of circles in the plane with center $(-2,3)$. Furthermore, let $P(C_1,C_2)\colon C_1$ and $C_2$ have exactly one ...
0
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1answer
52 views

Use calculus to derive area of circle using n triangles

This is a homework question I am struggling with... Let $n$ be a positive integer, and cut the circle into $n$ equal sectors. In each sector there is an isosceles triangle formed where the edges of ...
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2answers
64 views

Construction of a common mean proportional

"Given four points, A, B, C, D in order on a straight line construct a point P on BC such that PA.PB = PC.PD" I assume the end result is to have two right angled triangles AXP with X perpendicular to ...
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2answers
30 views

Caclulate X,Y coordinates of point after rotation around another point of given degrees

There are Two Points A and B. The linear distance between the points is R. I have the ...