why 360 degrees?
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Dr. Math FAQ:
segments of circles
Browse High School Conic Sections, Circles
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Selected answers to common questions:
Find the center of a circle.
Is a circle a polygon?
Volume of a tank.
Why is a circle 360 degrees?
- Common Internal Tangent [03/29/2002]
Two circles with radii 9 and 6 are 2 cm. apart. Find the length of the
common internal tangent.
- A Complete Proof about Tangential Circles [06/05/1998]
Can you show me a proof, with full justification, of the following
theorem? Two circles of the same radius touch at A ...
- Complete This Square: x^2 + y^2 - 6x + 2 = 0 [03/16/2003]
I thought completing the square only involved quadratic functions,
such as f(x) = ax^2 + bx + c = 0. This question relates to the
equation of a circle...
- Completing the Square in a Hyperbola Equation [01/04/2004]
A discussion of how to complete the square and how to apply it to the
equation of a hyperbola such as 4(x^2 – 4x) - 9(y^2 + 6y) = 101.
- Conical Vertex? [03/27/2003]
What is the point at the tip of a cone called?
- Conic Sections and Parallel Lines [3/18/1995]
Our teacher told us there was a way to cut a cone with a plane to get
parallel lines. Another teacher in the department can do it
algebraically, but no one can do it physically. Is there such a plane in
reality or only in theory?
- Connection Between Circumference and Surface Area [05/08/1998]
Can you explain the connection between the circumference of a circle and
the surface area of a sphere?
- Constructing an Ellipse [04/15/1997]
How do you draw an ellipse?
- Constructing a Tangent to a Circle [03/19/1999]
Construct a tangent to a circle through a given point not on the circle.
- Constructing a Tangent to a Circle, Continued [03/26/2013]
The proof of a tangency construction leaves a couple puzzled. Doctor Peterson
explains how it relies on a property of angles inscribed in semi-circles.
- Constructing Axes of an Ellipse with Straightedge and Compass [01/23/2006]
Presented with the graph of an ellipse, is there a way to determine
the axes by using straightedge and compass?
- Convert Degrees to Radians [7/21/1996]
How do you convert degrees to radians, and vice versa?
- Converting RPM to MPH and MPH to RPM [04/07/2002]
What is the formula for converting RPM's from an 'X' inch diameter
wheel into miles per hour?
- Coordinate Geometry and Distance Formula [10/02/2002]
I need to find the center and radius of the following equations and
then graph them: (x-3)^2 + (y+4)^2 - 9 = 0; x^2 + y^2 = 36.
- Coordinate Geometry of Circles [02/26/2003]
The line with equation y = mx is a tangent to the circle with equation
x^2 + y^2 - 6x -6y +17 = 0. Find the possible values of m.
- Counting Regions Formed by Chords of a Circle [05/19/1998]
Determining the number of regions formed by connecting n points on the
circumference of a circle.
- Cow Grazing Half the Circle: Newton-Raphson Method [01/18/1998]
Assume a perfect circle filled with grass and a cow tied with a rope to
the fence around it...
- Creating Tangents to Circles [10/24/2007]
I know how to draw a tangent to a circle from a point outside the
circle. How can I create four distinct tangents that are common to two
- Cutting a Circle out of a Square [2/14/1996]
What is the area (to the nearest square centimeter) of the largest circle
that can be cut from a square piece of sheet metal 73cm. on each side?
Explain how you determined this.
- Cutting a Wedge out of a Disk to Make a Cone [12/05/2005]
A cone can be formed by cutting a wedge out of a disk and then rolling
the remaining part into the cone shape. How can I determine how big
the wedge should be to make a cone of given dimensions?
- Cyclic Quadrilaterals [8/30/1996]
A cyclic quadrilateral touches a circle at each vertex. What angles do
these points make with the centre of the circle?
- Cycloid [01/30/1998]
What is a cycloid and what does it do?
- Defining an Ellipse, Continued [04/16/2013]
A student wonders why a sum of squares describes ellipses. Doctor Peterson
elaborates on a previous conversation about the general equation, in which he
sketched the system as a loop wrapped around two anchor points.
- Defining a Parabola with Three Points [05/09/2009]
Given three distinct points, one of which is the vertex of a parabola,
is there only one unique parabola that passes through the points?
- Definition of an Ellipse [1/4/1995]
I have a question concerning the concept of an ellipse. It is said that
the equation for an ellipse is Pf + Pr= 2a where P is a point on the
ellipse and f and r are the points of the foci. How do we know that this
is true, that is that Pf + Pr = 2a? How did we come up with the constant
- Deformed Bullet [04/11/2002]
If you initially have a circle and it gets smushed into an ellipse,
how do you determine the diameter of the initial circle, knowing the
major and minor diameter of the ellipse?
- Degenerate Conics [03/04/1998]
Identifying the degenerate cases for the graphs of equations in conic
- Degenerate/Nondegenerate Figure [10/27/2001]
We need to know what a nondegenerate circle is. (We're trying to decide
whether this is a model of incidence geometry, but don't know the
- Degrees in a Circle [09/22/1997]
Why does a circle measure 360 degrees - is there a special reason for
- Derivation of the Equation of an Ellipse [06/23/1999]
How can I derive the equation of an ellipse from its definition?
- Deriving the Hyperbola Formula [04/27/1998]
When speaking of hyperbolas, why does C^2 = A^2 + B^2?
- Descartes Circle Theorem [01/15/2008]
What is the radius of the largest circle which can be inscribed within
the area formed by three mutually-tangent circles, in terms of the
radii of the three circles?
- Describe the Locus [03/28/2002]
What is the locus of all points in a plane two inches from a point A?
- Designing and Building a Cone Frustum [03/24/2004]
I need help making making a pattern for a frustum shape to protect a
large piece of equipment. How can I find the distance between the top
and bottom arcs in a straight line?
- Determining Cone's Original Dimensions from a Slice [05/18/1999]
Given the inside and outside arc lengths and the thickness of a truncated
cone, find the inner and outer radii and the angle.
- Determining the Equation of a Circle [05/12/2000]
How can I determine which of five equations describes the set of all
points (x,y) in the coordinate plane that are a distance of 5 from the
- Diameter of a Ball [11/25/2001]
A child rolls a ball on a level floor 4.5m to another child. If the ball
makes 15 revolutions, what is its diameter?
- Diameter of a Circle Circumscribed Around a Triangle [05/13/1998]
Applying the Pythagorean Theorem to find the diameter of the circle
circumscribed around a triangle with side lengths 25, 39, and 40.
- Diameter of Flying Saucer [5/27/1996]
We are constructing an oval racetrack in Atlanta...
- Diameter of the Base of a Cone [08/12/1998]
How do you find the formula to calculate the diameter of the base of a
cone of nine degrees at various lengths?