For questions conserning circles. A circle is a curve composed of points in a plane that are at a fixed distance from a fixed point.

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1answer
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Angle of an arc in a circle

A mathematics book on circle states one of the properties of circle as follows : "angle formed by two chords intersecting in a circle is equal in degrees to one-half the sum of its intercepted arcs." ...
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2answers
133 views

How do I proof that $\angle ABP =\angle AP'B$ and that $P$, $Q$, $Q'$ and $P'$ are on 1 circle?

Given is a circle with center $M$ and a diameter $AB$. $k$ is the tangent to the circle at point $B$. On the circle there are two points called $P$ and $Q$, such that $P$ and $Q$ are both on the same ...
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1answer
101 views

Euclidean geometry: Circle incribed in a circle

Circle $c_2$ - with center $N$ - is inside circle $c_1$ and is tangent to circle $c_1$ - with center $M$ - in $P$. The line $l$ intersects $c_1$ at points $A$ and $D$ and $c_2$ at points $B$ and $C$. ...
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2answers
481 views

Circle touching the $y$-axis passing through two points

How to find the equation of the circle touching the $y$-axis given that it passes through two particular points?
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1answer
100 views

What is the meaning of $(x^2+y^2)^n$? Is this an already known geometric object?

We all know that $x^2+y^2=r^2$ is a circle. What does $(x^2+y^2)^2$ signify? In general, what is $(x^2+y^2)^n$?
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1answer
122 views

Simple arc/saggita/chord relation rearrangement

I'm stuck with something that I feel should be trivial. Consider the diagram on this page: http://mathworld.wolfram.com/CircularSector.html There are some pretty simple relations between the ...
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1answer
945 views

Proving triangles congruent with circles

I have a proof that looks like the following, not really sure where to start/how to solve. Any help would be appreciated. Given: circle $S$ and circle $T$ intersect at $M$ and $O$. Prove: $\triangle ...
7
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2answers
342 views

Unequal circles within circle with least possible radius?

It is the classical will-my-cables-fit-within-the-tube-problem which lead me to the interest of circle packing. So basically, I have 3 circles where r = 3 and 1 circle where r = 7 and I am trying to ...
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3answers
144 views

Circle equation with sine without parametric equation

I had to integrate an area delimited by a quarter of a circle, something like this: http://www.wolframalpha.com/input/?i=integrate+10+-+sqrt%2864+-+x%5E2%29+dx+from+0+to+5 Which comes from the ...
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2answers
54 views

Calculating a circle's radius from one point and two circles on it's circumference

Suppose that there are four points $A, B, C, D$. A circle of radius $r_A$ surrounds point $A$, a circle of radius $r_C$ surrounds point $C$, and a circle of radius $|DB|$ surrounds point $D$. ...
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3answers
286 views

If a circular plate is cut along a chord equal in length to the radius, what is the ratio of the areas of the two parts?

A circular metal plate is cut into two segments along a chord equal in length to the radius. What is the ratio of the areas of the two segments. The question above was give in a maths textbook under ...
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2answers
732 views

finding the radius of a circle that intersects a sphere

I'm an openGL programmer, trying to construct a sphere in specific circumstances. Imagine a sphere sliced up into numerous flat horizontal circles. Given a position along the vertical (Y) axis of ...
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1answer
567 views

Crescent Geometry (Dividing into Regions)

I was given the following problem: "Using one straight line we can divide a crescent (a.k.a. lune) into a maximum of 3 regions. Using two straight lines we can divide a crescent into a maximum of 6 ...
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3answers
155 views

General form of a circle

My math teacher taught me that the general form (equation) of a circle is: $$ ax^2+by^2+cx+dy+e=0 $$ He also asked us this: If the product of $c$ and $d$ is negative, then what 2 quadrants can the ...
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2answers
117 views

Four circles & a square in a circle

Radius of the big triangle is $2$. ABCD is a square. What is the difference between $T_{1}$ and $(M_{1}+M_{2})$. I have solved it already though I don't know if my answer is right or wrong. My ...
4
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2answers
150 views

Evaluate $I = ∫∫ 1/((x^2 + y^2)^{n/2}) dxdy$

Evaluate the double integral $$ I = \int\int_D \frac{1}{(x^2 + y^2)^{n/2}} dxdy .$$ where $n$ is an integer and $D$ is the region of the plane bounded by two circles centered on the origin and ...
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1answer
57 views

Condition for this set of points

This is for a calculator experimental prob. simulation. So, there is circle in a square and the circle is touching all 4 sides of the square. We need to first choose a coordinate system (two ...
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4answers
498 views

Direct method to find the equation of a circle.

Suppose we are given four concyclic points or two lines which intersect the axes in concyclic points. Many a times, one point has a variable as a co-ordinate. Suppose the concyclic points are ...
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2answers
539 views

In the figure,O is the centre of a circle and BCD is tangent to it at C. Prove that ∠BAC + ∠ACD = 90°.

I am a beginner to these type of questions relating to tangents ..... Thats all.
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1answer
168 views

how to find sin13° cos13° tan13° cot13° with trigonometric circle.

I have problem finding sin(13°) cos(13°) tan(13°) cot(13°)with trigonometric circle. I have to draw the circle with a triangle on it but I can't get the right thing.
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1answer
59 views

Compute angle and radius of a circular segment

I need some help computing the angle and radius of a (given) circular segment. All I have is a start point $P_0 = (0,0)$ where the circular segment begins, at the origin. The length of circle arc ...
2
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3answers
102 views

Finding the center of a circle

Let us suppose there are two straight lines having equation x=5 and y=7 and a circle is drawn such that these two straight lines are tangents to the circle. Now we are required to find the center of ...
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2answers
112 views

Length of chord in circle [closed]

In Figure 3, arc CD is a semicircle. AB is perpendicular to CD, BC = 3, BD = 4. Then the length of AB = a) 3.25 b) 4.56 c) 3.46 d) 7.00
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1answer
115 views

maximum number of smaller circle possible from a big circle

a big circle has radius 5 cm is cut down into smaller circles of radius 1 cm .How many maximum number of smaller circle possible? How it is calculated?
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1answer
57 views

Bicentric quadrilaterals

I'm trying to prove that a 'tangential' quadrilateral (i.e. one with an in-circle) whose area is given by Brahmagupta's formula for a cyclic quadrilateral is also cyclic (and thus 'bicentric').
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1answer
133 views

Derivation of the length of an arc formula

My textbook says that the radian measure of an angle is the ratio: $\theta = \frac{s}{r}$ Where s is a portion of the entire circumference, and r is the radius. So essentially the arc length is thus: ...
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2answers
72 views

Is point exist in circle?

Let us consider x and y is a point and then make a radius of some value r.If suppose i had a ...
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3answers
193 views

Calculate area of a specific part of a circle?

I am trying to calculate the area of a specific region inside a circle. The region, in this case, is the green area inside the circle. The given material is the equation, radius and the center of ...
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1answer
39 views

How to build a circle if…

We have a point and two lines. Build a circle which has to pass through the point and has to be tangent to the given lines. I appreciate any help and explanations!
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2answers
62 views

Relation between the radius and the area of tangential polygon

I've recently found a book with loads of formulas for triangle area, but unfortunaly the formulas were just listed, there wasn't a proof for them. I've tried to proof them. But I've stopped at one of ...
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5answers
755 views

Mensuration question about a hoop resting on a staircase

I came across a question recently: A hoop, as shown in the diagram, rests vertically at stair case. Note: AB = 12 cm, and BC = 8 cm. Find the radius of the hoop. Figure (hand-made): This is ...
0
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1answer
105 views

Positioning Points Based On Distances (Intersecting Circles)

I have a series of points, which represent mobile devices within a room. Previously I have systematically emitted a ping from each and recorded the time at which it arrives at the others to calculate ...
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2answers
495 views

Why the unit circle in $\mathbf{R^2}$ has one dimension?

When I was reading 'Convex Optimization, Stephen Boyd', I was wondering of following steps Consider the unit circle in $\mathbf{R^2}$, $i.e.$, $\{x\in\mathbf{R^2}|x^2_1+x^2_2=1\}$. Its affine hull ...
2
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2answers
554 views

Ellipse bounding rectangle

I'm trying to find the ellipse that bounds a rectangle in a way that the "distance" between the rectangle and the ellipse is the same vertically and horizontally. Here is an image to illustrate what ...
5
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1answer
844 views

How is the Radian measure of angles derived/defined?

I'm currently studying the foundation of trigonometry (angles and their measures) and I've just been told that $\pi$ is the ratio of a circle's circumference to its diameter, so: $\pi =\dfrac ...
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2answers
1k views

Software to draw easily sectors with angle on it

I want to draw a sector with the angle on it. I have tried several tools but didn't find any easy way of doing it.
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3answers
99 views

the length of the circumference of a circle always bears a constant ratio to its diameter

I'm reading SL Loney's plane trigonometry book and I arrived at a theorem saying : "the length of the circumference of a circle always bears a constant ratio to its diameter." Now, in this proof he ...
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4answers
1k views

Quarter-Circle inscribed in a Square.

Quadrilateral ABCD is a square with a side length of 4 cm. A quarter-circle with radius 4 cm and centered at D connects A and C, and a quarter-circle with the same radius centered at B also connects A ...
0
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1answer
291 views

Given three points, find the arc length of a section between two intersecting lines.

I have three points, one being the center, and the other two are end points on a line drawn to the center. I need an equation that provides $\Theta$. In this drawing $(x_1, y_1)$ is the center.
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1answer
600 views

Find if point lies into given sector of circle

I am looking for a good method to find out if a specified point lies within a specified circle. The situation looks as follows: Where the line at r has a given heading (60°). I now want to find out, ...
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2answers
445 views

formula for Tangent point of two arcs

Please Help finding proper formula for Tangent point of two arcs. 1st arc R = .030; 2nd R = 0.015, need to get mathematical explanation on how to get (0.02494, 0.01333) point. Assume that starting ...
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2answers
64 views

Check degrees within circle range

What would be the most performing way to check whether a number of degrees (e.g. $10^\circ$) is within a range of degrees $\pm 30^\circ$ outgoing from $355^\circ$? For a better understanding of my ...
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2answers
50 views

Get the coordinate value of intersecting points

I have a square buy 100 cm in side, now a cricle is drawn taking the center of the square and having radus of 50cm which touches the borders of the square as you can see above, Now imagine another ...
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1answer
498 views

How many ways to find the center of an inscribed circle?

I want to find the coordinates of center of the inscribed circle triangle $ABC$, where $A(-274,-253)$, $B(-1,7)$, $C(14,7)$. I tried First way. We have $c = AB=377$, $a = BC=15$, $b = AC=388$. Let ...
3
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1answer
78 views

Prove that $PT$ bisects $\angle{ATB}$ with two touching circles.

I'm having some trouble figuring out this apparently easy question: Two circles touch internally at $T$. $TP$ is a chord of the smaller circle and the tangent at $P$ cuts the larger circle at $A$ ...
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1answer
154 views

Intersecting Circles Theorem (about 1983 AIME #14's solution)

Please consider this problem: http://www.artofproblemsolving.com/Wiki/index.php/1983_AIME_Problems/Problem_14 Now look at solution 2 - it assumes that A, B, and R are co-linear, but does not prove ...
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1answer
208 views

Find the point of a circumference following the line from center to a point in the circle

The purple circle dignifies a known center point. If I choose a point at random inside the circle, is it possible find the orange square (The point where the green line intersects with the ...
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1answer
93 views

explaining the resriction $b<a<2b$ in a triangle

I saw in a book that if $ABC$ is an isosceles triangle $(AB=AC)$ and the triangle is tangent to a circle in points $D,C$ and $AC$ is intersecting the circle in point $E$; $AC=a$, $BC=b$ so it has ...
0
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1answer
32 views

Figuring out the side of a triangle

I'm having trouble on this problem I don't know how to set it up. I know XO=2 and OB=6. I'd appreciate any hints.
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2answers
97 views

Number of Equilateral triangles in circle with 42 evenly spaced points?

I know that the answer is 42/3 = 14 points, or in general for a circle with N points it is N/3, but I don't know why it actually works. Why is the number of equilateral triangles for a circle with N ...