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How is that any line intersecting the interior of a given circle is a secant of that circle?
Wiki User
∙ 15y ago
Any line that enters a circle (and is not a tangent) must cross its boundary twice; once to enter, once to exit. Since a secant is a line segment that joins two different points on a curve, such a line as above is a secant.
Wiki User
∙ 15y ago
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What do intersecting lines add up to?
360 degrees around a given point
What is the derivative of y equals tan x?
Given y = tan x: dy/dx = sec^2 x(secant of x squared)
What is the locus of point equidistant from two intersecting lines?
The locus in a plane is two more intersecting lines, perpendicular to each other (and of course half-way between the given lines.
What is the name given to the ordered pair of real number that two intersecting line have in common?
The intersection or point of intersection
What can be said about the relationship between triangle and circles?
Exactly one circle can be inscribed in a given triangle.Many triangular shapes can be inscribed in a given circle.
What is an orthocircle in math?
This is an uncommon term. I believe it means a circle which intersects a given circle orthogonally, i.e., with their arcs intersecting at 90 degrees.
The circular boundry of the circle is called the?
The boundary which defines the area of a circle is known as the circumference of the circle.However if one wants to be precise, the circumference is the distance around the outside of the circle, not the circle itself. The term "circle" itself means the boundary. It has an interior and an exterior.A circle can be defined as all the points that are the same distance from a given point.
What do intersecting lines add up to?
360 degrees around a given point
What is the derivative of y equals tan x?
Given y = tan x: dy/dx = sec^2 x(secant of x squared)
What is the circumference of the given circle?
We've not been given a circle.
What is the set of all points in a plane that are a given distance from a given point?
That's a "circle". The given distance is the circle's radius, and the given point is the circle's center.
What is the locus of point equidistant from two intersecting lines?
The locus in a plane is two more intersecting lines, perpendicular to each other (and of course half-way between the given lines.
What name is given to half a circle?
semi circle
What is the formula to find interior angles?
there is no fix formula for this..........you have to check that what is given to you in the question. According to the given you have to find the interior angle.
How do you find the area of a circle when the radius is unknown?
By using the other information supplied about the circle to calculate either its radius (from which its area can be calculated) or its area (if the circle is similar to another with a given area and some ratio between the two circle is given):If the diameter is given: radius = diameter ÷ 2If the circumference is given: radius = circumference ÷ 2πIf the circle is similar to another circle which has a given area, and the length ratio is given; square the length ratio to get the area ratio and apply to the given area.
Is brocli a tuber?
A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are the same distance from a given point called the center. The common distance of the points of a circle from its center is called its radius. A diameter is a line segment whose endpoints lie on the circle and which passes through the centre of the circle. The length of a diameter is twice the length of the radius. Circles are simple closed curves which divide the plane into two regions, an interior and an exterior. In everyday use the term "circle" may be used interchangeably to refer to either the boundary of the figure (known as the perimeter) or to the whole figure including its interior, but in strict technical usage "circle" refers to the perimeter while the interior of the circle is called a disk. The circumference of a circle is the perimeter of the circle (especially when referring to its length). A circle is a special ellipse in which the two foci are coincident. Circles are conic sections attained when a right circular cone is intersected with a plane perpendicular to the axis of the cone. A chord of a circle is a line segment whose two endpoints lie on the circle. The diameter, passing through the circle's centre, is the the largest chord in a circle. A tangent to a circle is a straight line that touches the circle at a single point. A secant is an extended chord: a straight line cutting the circle at two points. An arc of a circle is any connected part of the circle's perimeter. A sector is a region bounded by two radii and an arc lying between the radii, and a segment is a region bounded by a chord and an arc lying between the chord's endpoints.The circle has been known since before the beginning of recorded history. It is the basis for the wheel which, with related inventions such as gears, makes much of modern civilization possible. In mathematics, the study of the circle has helped inspire the development of geometry and calculus. Early science, particularly geometry and astronomy/astrology, was connected to the divine for most medieval scholars, and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles. Some highlights in the history of the circle are: * 1700 BC - The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 256/81 as an approximate value of π.[1] * 300 BC - Book 3 of Euclid's Elements deals with the properties of circles. * 1880 - Lindemann proves that π is transcendental, effectively settling the millennia-old problem of squaring the circle.[2]The circle is the shape with the largest area for a given length of perimeter. (See Isoperimetric inequality.) * The circle is a highly symmetric shape: every line through the center forms a line of reflection symmetry and it has rotational symmetry around the center for every angle. Its symmetry group is the orthogonal group O(2,R). The group of rotations alone is the circle group T. * All circles are similar. * ** A circle's circumference and radius are proportional. ** The area enclosed and the square of its radius are proportional. ** *** The constants of proportionality are 2π and π, respectively. * The circle centered at the origin with radius 1 is called the unit circle. * ** Thought of as a great circle of the unit sphere, it becomes the Riemannian circle. * Through any three points, not all on the same line, there lies a unique circle. In Cartesian coordinates, it is possible to give explicit formulae for the coordinates of the center of the circle and the radius in terms of the coordinates of the three given points. See circumcircle. [edit] Chord properties * Chords are equidistant from the center of a circle if and only if they are equal in length. * The perpendicular bisector of a chord passes through the center of a circle; equivalent statements stemming from the uniqueness of the perpendicular bisector: * ** A perpendicular line from the center of a circle bisects the chord. ** The line segment (circular segment) through the center bisecting a chord is perpendicular to the chord. * If a central angle and an inscribed angle of a circle are subtended by the same chord and on the same side of the chord, then the central angle is twice the inscribed angle. * If two angles are inscribed on the same chord and on the same side of the chord, then they are equal. * If two angles are inscribed on the same chord and on opposite sides of the chord, then they are supplemental. * ** For a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle. * An inscribed angle subtended by a diameter is a right angle. * The diameter is the longest chord of the circle. [edit] Sagitta properties * The sagitta (also known as the versine) is a line segment drawn perpendicular to a chord, between the midpoint of that chord and the circumference of the circle. * Given the length y of a chord, and the length x of the sagitta See also: Power of a point * The chord theorem states that if two chords, CD and EB, intersect at A, then CA×DA = EA×BA. * If a tangent from an external point D meets the circle at C and a secant from the external point D meets the circle at G and E respectively, then DC2 = DG×DE. (Tangent-secant theorem.) * If two secants, DG and DE, also cut the circle at H and F respectively, then DH×DG = DF×DE. (Corollary of the tangent-secant theorem.) * The angle between a tangent and chord is equal to the subtended angle on the opposite side of the chord. (Tangent chord property.) * If the angle subtended by the chord at the center is 90 degrees then l = √2 × r, where l is the length of the chord and r is the radius of the circle. * If two secants are inscribed in the circle as shown at right, then the measurement of angle A is equal to one half the difference of the measurements of the enclosed arcs (DE and BC). This is the secant-secant theorem. *
Locus of a point equidistant from two intersecting lines?
the pair of lines bisecting the angles formed by the given lines
