Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [circles]

For questions concerning circles. A circle is the locus of points in a plane that are at a fixed distance from a fixed point.

0
votes
0answers
11 views

Find a point on a circle which contains a rectangle using another point, the angle between the two and the rectangle's dimensions

I'm trying to construct a mathematical formula that will calculate a point (x,y) on a circle which contains a rectangle with a width ...
0
votes
0answers
37 views

Unit circle and cone

I know that in the following question, I would consider finitely many cases depending on where the points are located, but I would appreciate help on this: a) How would I define a unit circle in a ...
1
vote
0answers
30 views

Probability of obtuse triangles formed on a circle

There are 16 equally spaced points on the circumference of a circle. If 3 points out of these 16 points are selected randomly, What is the probability that they will form an obtuse angled triangle?
1
vote
0answers
54 views

Where does the square intersect with the circle?

A circle is drawn with center at origin, O, and radius $6$ cm. Find the coordinates of all intersections of the circle with an origin centered square of side length $10$ cm whose sides are parallel ...
3
votes
2answers
100 views

How to find $k$ such that the line $y=x-2-k$ is tangent to the circle given by $x^2+(y+2)^2=4$?

I have the circle $x^2+(y+2)^2=4$ and the line $y=x-2-k$. How would you find a $k$ value that would allow the second equation to sit tangent to the circle? There should, in theory, be only two ...
1
vote
0answers
20 views

What is the coordinate value after moving counterclockwise by distance $d$ from a coordinate on the ellipse?

Let me define an ellipse function as follows: Assuming $a \ge b$, $$ f(x,y) = \frac{(x-x_0)^2}{a^2} + \frac{(y-y_0)^2}{b^2} = 1,$$ where $(x_0,y_0)$ is the origin of the ellipse, and $a$ and $b$ are ...
0
votes
4answers
34 views

Why is the centre of a circle: (x + a)² + (y + b)² = c², (-a, -b)

1) Why is the centre of the circle: (x + a)² + (y + b)² = c² (-a,-b) ? 2) What is a good way of remembering that the centre of the circle: ...
0
votes
3answers
42 views

Square with circle

$$ABCD - square $$ $$M\in AB, N \in AD, P \in DC : BM = AN = DP$$ I have to show that the intersect of the diagonals is the centre of the circumscribed circle around NMP. I have noticed that NMP is ...
0
votes
3answers
13 views

Circumscribed circle

$\triangle ABC: \angle CAB = 45^o, BC = 9$. I have to find the diameter of the circumscribed circle. I thought about an hour, but I can't think up anything. I would be very grateful if you can help me!...
0
votes
3answers
61 views

How to check if a line is a tangent to a circle?

Is there a short and simple way to check if a line is a tangent to a circle, without complicated distance formulae? A solution to a question in my book says that for a circle $(x-at^2)(x-a/t^2) + y(y-...
-3
votes
0answers
25 views

3 circles. Show that the centre of the circle which touches one circle internally and the other circle externally lies on a specific path [on hold]

$C_1 \Rightarrow$$x^2+y^2=4$ $C_2 \Rightarrow $$x^2+y^2=2x$ Show that the Centre of $C_3$ Lies on the curve $8x^2+9y^2-8x-16=0$ $\star\text { $C_2$ touches $C_1$ internally.}$ $\star\text{ $C_3$ ...
1
vote
1answer
27 views

Calculating point on circle given angle and distance traveled without calculating radius

I want to calculate the X,Y coordinates of a point on a circle given only the distance and angle traveled, without calculating the radius as an intermediate step. My starting point (0,0) is at the ...
-4
votes
0answers
16 views

the line passing through center of circle cutting through the circumference, what are the co-ordinates [closed]

I have a circle with radius R and center C at origin, i.e. (0, 0). If a point P lies ...
1
vote
0answers
48 views

Approximation for the equation of an imperfect circle

Given two random points $(x_0,y_0)$ and $(x_1,0)$ and some condition, I have an equation $C[(x-x_0)^2+(y-y_0)^2]=[(x-x_1)^2+y^2]^2$ which is a perfect circle if I ignore the power (2) on the RHS. ...
3
votes
1answer
59 views

Prove that $\frac{1}{AA'}+\frac{1}{BB'}+\frac{1}{CC'}<\frac{2}{R'-OO'}$

Let $\Delta ABC$ is acute triangle has $AB>AC$ and $O$ is incircle of $\Delta ABC$ with radius $R$, $O'$ is circumcircle of $\Delta ABC$ with radius $R'$. $OA\cap BC=A';OB\cap AC=B';OC\cap AB=C'$ ....
1
vote
1answer
61 views

Problem about incentre of a triangle.

Through the incentre $I$ of triangle $ABC$ a straight line is drawn intersecting $AB$ and $BC$ at points $M$ and $N$, respectively, in such a way that the triangle $BMN$ is acute- angled. On the ...
0
votes
4answers
30 views

Calculating a circle area by rotating its diameter

I thought a circle as a set of dots . The circumference is about 314.16 dots long and the diameter 100 dots long. I am wondering if it is possible to calculate the area of a circle by rotating its ...
0
votes
1answer
19 views

Analogous of Power of Point in Euclidean Geometry in high dimension

While playing around with dot product in 2D, I realized it's scalar projection behavior is directly related to power of point in Euclidean Geometry. I am wondering if there is any notion similar to ...
-1
votes
3answers
38 views

Circle Question [closed]

I feel like I am being really stupid here, so can anyone please help
-2
votes
3answers
39 views

Tangent on a circle [closed]

In really stuck on this maths problem. Any help would be appreciated
0
votes
0answers
34 views

Points uniformly distributed on a circle

We select randomly two points in the circumference (with length equal to 1) of a circle. Let $X,Y$ be those points (independent and uniformly distributed) and $D$ the arc distance between them. Since ...
-1
votes
1answer
32 views

If the equation for a circle is $8x+32y+y^2=-263-x^2$. What is the $x$-value? What is the $y$-value? What is the radius? [closed]

If the equation for a circle is $8x+32y+y^2=-263-x^2$ What is the $x$-value at the center? What is the $y$-value at the center? What is the radius?
0
votes
0answers
10 views

Finding trig solution to locate the center of an arc that intersects a given arc in the upper right quadrant

Circles with colinear (on X axis) centersWorking entirely in the quadrant where x and y are positive, I'm looking for a trig-based solution for something I can easily construct with a compass but can'...
1
vote
1answer
25 views

Logic of Step to Convert Rectangular Equation of Circle to Parametric

I recently learned in math class how to convert the rectangular equation of a circle into a parametric equation: $x^2+y^2=1$ $\cos^2(t)+\sin^2(t)=1$ $x^2+y^2=\cos^2(t)+\sin^2(t)$ $x^2=\cos^2(t)$ $...
0
votes
0answers
27 views

Is this formula correct or best practice?

I have used the formula $((x*x)/(y*2))+(y/2)$ to find the radius of a circle given values x and y on a cartesian plane. I cannot find this formula anywhere and while i know it works, is there a ...
2
votes
1answer
55 views

How long is this line making a loop?

Here I have this loop, made of parts of two different circles with radiuses $r_1$ and $r_2$, joined with two lines intersecting at $90$ degrees and touching the circles only in one point, as shown in ...
0
votes
1answer
22 views

Simple formula for radius of circumcircle from coordinates of 3 points

Given $A=(a_1,a_2), B=(b_1,b_2), C=(c_1,c_2)$, is there a simple formula to express the radius of the circumcircle of $ABC$? Note that you could compute the radius from the sidelengths as $\frac{abc}{...
1
vote
1answer
46 views

Symbol for cyclic quadrilateral

Is there a symbol to denote, say, $ABCD$ is a cyclic quadrilateral? (I very much doubt it.)
1
vote
1answer
26 views

How much displacement of x and y to satisfy a given value

Consider two circles $C_1((x,y),r)$ and $C_2((x_1,y_1),R)$ the two circles insects when the distance $d=\sqrt{(x-x_1)^2+(y-y_1)^2}$ between the two circles is less than $d < r+R$ I want to know ...
0
votes
2answers
20 views

Circle coordinate geometry question

The question states: Find the equation of the following circles: A circle has its centre on the line x + y = 1 and passes through the origin and the point (4,2). What I did to try to solve this is ...
0
votes
2answers
28 views

Prove that the four points are concyclic if they are harmonically related w.r.t. the midpoint of connecting line segment.

$(1)$$AB$ and $CD$ are two intersecting line segments, and $P$,$Q$ are their respective midpoints. If $AB$ bisects $\angle CPD$ and $PA^2=PB^2=PC.PD$, then prove that the points $A,B,C$ and $D$ are ...
-1
votes
1answer
16 views

Locus circle and equilateral triangle question

An equilateral triangle of side 25cm circumscribes a circle. Find the radius of the circle. I drew it out, and tried to create a right angled triangle and perform Pythagoras but it was not right, do ...
0
votes
1answer
17 views

Loci circle question

Im not sure how to answer this. PS AND PT are two tangents draw from a point P to a circle whose centre is O. Join PO and prove that PT = PS. I drew the diagram out and so I would end up with two ...
0
votes
1answer
38 views

Finding a point on a circle in 3D space which is a given distance away from another point

I am trying to find a point, lets call it $X = (x_1, x_2, x_3)$, on a circle in 3D space (with a center $C_1$, radius $r$ and unit vector $\vec{AX}$ perpendicular to the plane of that circle ) which ...
-3
votes
2answers
59 views

Number of rational points on ellipse [duplicate]

How to find the number of rational points on the circumference of ellipse $$ \frac{x^2}{9}+\frac{y^2}{4}=1 \,$$
0
votes
2answers
33 views

Calculate arc central angle given the center, radius, start and end points of the arc

How can I calculate the angle at the center of an arc knowing radius and center, start, and end points? I know how to do that if I have the length of the arc, but in my case I don't have it.
0
votes
1answer
26 views

How can determine if a angle is betwen two angles?

I have the following information about the problem Start point Size (angle between 0 and 360) End point (start point + size) Tarjet angle. The questions is how can determine if a tarjet angle is ...
3
votes
3answers
74 views

Why does $\vec{F(t)} \cdot \vec{v(t)} = 0$ lead to a circular motion?

Here is a mathematical proof that any force $F(t)$, which affects a body, so that $\vec{F(t)} \cdot \vec{v(t)} = 0$, where $v(t)$ is its velocity cannot change the amount of this velocity. Further, ...
2
votes
2answers
54 views

Find minimum perimeter of the triangle circumscribing semicircle

The following diagram shows triangle circumscribing a semi circle of unit radius. Find minimum perimeter of triangle My try: Letting $$AP=AQ=x$$ By power of a point we have: $$BP^2=OB^2-1$$ where $...
0
votes
1answer
50 views

How do you tell if an equation makes a circle?

For instance the equation, $$(x-3)^2+(y+4)^2=25$$ would be graphed as a circle. Is there a way to see that an equation creates a circle without graphing it? Is there a certain set of criteria it must ...
2
votes
2answers
54 views

Circle inscribed in a semicircle

There is black semicircle, which radius is $ R $. The red circle is tangentially inward to the semicircle and to the diameter in its center. The yellow one is tangent externally to the red circle, ...
0
votes
2answers
42 views

Circle drawn on focal chord of a parabola

Is it possible for a circle with diameter as any focal chord of a parabola to cut the parabola at 4 points (2 being the extremities of the focal chord)? We were asked to find the product of the ...
4
votes
3answers
71 views

An equilateral triangle is drawn in a circle with one of its vertices on the diameter. What is $x$ in the figure?

$O$ is the center of the arc $AEC$; $ABD$ is an equilateral triangle $\angle ACB = 45^o$; $|BO|= 6$ cm Find $|DC|=x$ I tried completing the square, drawing radii to the intersection points, ...
1
vote
2answers
48 views

Extremal Area and side length of a triangle in a circle

Given a Circle $B_r$ and a triangle $\triangle ABC$ in it with two fixed (immovable) points $A$ and $B$. The third point $C$ can be moved on the circle. I want to prove the following equivalence: (for ...
1
vote
1answer
37 views

Prove that $AD \cdot AD' = AE \cdot AE'$.

Circle diameter $BC$ cuts side $AB$ and $AC$ of $\triangle ABC$ respectively $C'$ and $B'$. $E$ and $E'$ are points respectively on $BC$ and the circumcircle of $AB'C'$ such that $EE'$ passes through $...
0
votes
2answers
42 views

CIRCLES (FINDING ANGLES)

In the given figure a semi-circle is drawn with centre M and AB is diameter. If $\measuredangle MQN= \measuredangle MPN= 10^\text{o}$ and $\ \measuredangle AMQ=40^\text{o}$, then the measure of $\...
0
votes
2answers
55 views

What are the properties that make circles similar?

At first, when thinking about similar circles I tried extending the properties of similar triangles to circles to reason that all circles are similar. The properties of similar triangles are as ...
4
votes
2answers
57 views

Prove that $DD' \parallel EE'$.

$BB'$ and $CC'$ are altitude of $\triangle ABC$. Point $D'$ is outside $\triangle ABC$ such that $D'B \perp AB$ at $B$ and $D'C \perp AC$ at $C$. $AD \cap B'C' = \{E\}$ and $AD' \cap BC = \{F\}$. ...
1
vote
2answers
77 views

Solving a System of Quadratic Equations for Sound Triangulation

I am currently attempting to solve a system of quadratic (and linear) systems that I have run into while trying to triangulate sound. My hypothetical setup includes 3 sensors on a perfectly ...
1
vote
0answers
15 views

Relationship between a circle inscribed in a square and a sphere inscribed in a cylinder

The ratio of the area of a circle to the area of the square it is inscribed in is equal to ${\pi\over 4}$ and the ratio of the volume of a sphere to the volume of the cylinder it is inscribed in is $2\...