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
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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
31 views

Area of rectangle? [on hold]

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 ...
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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 ...
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votes
0answers
17 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 ...
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
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2answers
34 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 ...
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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 ...
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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.
0
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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.
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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 ...
8
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6answers
476 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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1answer
32 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
35 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 ...
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vote
2answers
29 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
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\\ ...
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votes
4answers
74 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 $\pi$
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vote
4answers
43 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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vote
3answers
62 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
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 ...
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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 $ABC$, ...
4
votes
4answers
127 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
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 ...
1
vote
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
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
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*}
2
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0answers
22 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
119 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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vote
2answers
32 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
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= ...
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 ...
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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 ...
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vote
2answers
53 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
49 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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votes
1answer
30 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 ...
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2answers
27 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 ...
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votes
1answer
80 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 ...
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votes
1answer
18 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 ...
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1answer
20 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
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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
45 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
56 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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votes
2answers
28 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... ...
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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
53 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 ...