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 TOPICS This page:   conic sections,   circles    Search   Dr. Math Shortcuts:   why 360 degrees? See also the Dr. Math FAQ:   circle formulas and   segments of circles Internet Library:   conic sections,   circles HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Conic Sections, Circles Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     About ellipses.     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 non-overlapping circles? 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 of 2a? 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 form. 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 definition.) Degrees in a Circle [09/22/1997] Why does a circle measure 360 degrees - is there a special reason for this calculation? 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 point (-3,4)? 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? Page: []

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