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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2
votes
0answers
80 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
4answers
171 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 ...
1
vote
2answers
65 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
49 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
votes
2answers
27 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 ...
1
vote
1answer
45 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 ...
1
vote
2answers
65 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
votes
1answer
76 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 ...
-1
votes
1answer
61 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
votes
2answers
33 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
votes
1answer
130 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
108 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
29 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) $.
1
vote
0answers
45 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 ...
2
votes
0answers
50 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
votes
1answer
62 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. ...
0
votes
2answers
105 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
27 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*} ...
1
vote
1answer
55 views

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 ...
2
votes
1answer
33 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
votes
1answer
54 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 ...
1
vote
0answers
39 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: ...
2
votes
2answers
100 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
votes
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 - ...
0
votes
1answer
28 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 ...
1
vote
2answers
51 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 ...
1
vote
2answers
26 views

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? ...
0
votes
1answer
87 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 ...
0
votes
0answers
25 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 ...
1
vote
0answers
39 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
votes
1answer
81 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 ...
1
vote
2answers
79 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 ...
0
votes
2answers
207 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 ...
0
votes
2answers
69 views

Four complex numbers $z_1,z_2,z_3,z_4$ lie on a generalized circle if and only if they have a real cross ratio $[z_1,z_2,z_3,z_4]\in\mathbb{R}$

Let $[z_1,z_2,z_3,z_4]$ denote the cross ratio of the complex numbers $z_1,z_2,z_3,z_4\in \mathbb{C}$. Show that the distinct points $z_1,z_2,z_3,z_4\in\widehat{\mathbb{C}}$ lie on a generalized ...
-1
votes
1answer
65 views

Finding Chord Length with only points on circumference,radius and center

I have a table of sin and cos values. I know that the radius of the cirlce is 1. The center is 0. I'm trying to figure out the CHORD length between the points on the circumference. E.g. of points ...
0
votes
1answer
88 views

Calculate coordinates of a point on a circular arc

I have following dilemma I need to solve for my software: I have a circular arc, and I do know these: x,y coordinates of startpoint of the arc x,y coordinates of endpoint of the arc x,y coordinates ...
1
vote
3answers
121 views

Finding the equation of a circle given two points on the circle

11. Find the equation of the circle which touches $x^{2} + y^{2} - 6x + 2y + 5 = 0$ at $(4, -3)$ and passes through $(0, 7)$. My textbook has a worked example for obtaining the equation of a ...
1
vote
1answer
69 views

Proof of Compound Angle from Ptolemy's Theorem

I have a query regarding a proof I'm reading on the additive Sine compound angle formula, which uses Ptolemy's theorem. http://www.cut-the-knot.org/proofs/sine_cosine.shtml I'm looking at the ...
3
votes
5answers
598 views

Technique for proving four given points to be concyclic?

While making my way through an exercise, I stalled on question 7: 7. Prove that the points $(9, 6)$, $(4, -4)$, $(1, -2)$, $(0, 0)$ are concyclic. The book does not provide any guidance on how ...
6
votes
2answers
488 views

Is a circle classified as an ellipse?

I read that an ellipse had $2$ focal points. So, I thought if a circle had $2$ points that were simply infinitesimally close together wouldn't it be classified as an ellipse? Help would be ...
0
votes
1answer
81 views

Draw the line segment joining the centers of two circles. Where does it meet the circles?

I'm trying to construct a line segment between two circles. Given each radius and $x$, $y$ center of each circle, how can I find the endpoints for the blue line segment?
0
votes
0answers
25 views

Work back from atan2 please?

I have input from 2 axis which range from -1.0 to 1.0 and I convert that into degrees using the below formula. degrees = Math.toDegrees(atan2(axis1, axis2)) so an input of 1.0 and 1.0 gives a ...
-3
votes
1answer
70 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 $x$? ...
2
votes
1answer
42 views

“Reverse engineering” of a geometric illustration

The following enigmatic illustration can be found here, unfortunately without any accompanied comment or short description: Can you deduce its meaning? What was the way it was constructed?
0
votes
1answer
30 views

Question in finding final position in circle

im having difficulty solving this problem right now, I tried couple of times but i couldnt figure it out, can you please help and explain? thank you
0
votes
1answer
40 views

Integration: Find length of curve using NINT

Here are the questions - For question 4, part (b) gives a unit circle. But I'm unable to proceed with parts (a) and (c), since the curve is double valued for -0.5 Also, for question 6, integration ...
2
votes
2answers
122 views

Covering 1/8 of a circle

A circle of radius 1 is given, and 8 semicircles of radius 1/2, like in this picture: What is the radius of the smallest circle that can cover shaded area? There was another problem involving the ...
4
votes
3answers
57 views

Inverse of an ordered pair?

Let $f: A \to B$ be a bijective function where $A = [0, 2\pi)$ and $B$ is the unit circle. Find the inverse of $f(\theta) = (\cos\theta, \sin\theta)$. I don't understand what it means to take the ...
1
vote
5answers
90 views

Find third point to make isosceles triangle with a specific area

Using points A(1,2) and B(-2,-2), find a third point, with a positive y-value, that makes ABC an isosceles triangle with area 10 units${^2}$. I have found AB to be 5 and used this as $r^2$ below.. ...
6
votes
1answer
98 views

What is the equation to evenly distribute circles in a spiral?

What is the equation to evenly distribute circles in a spiral? I have attached a picture to show what I am trying to achieve and need to know what the equation is for this.