Definition of radius of a circle

Radius The radius of a circle is defined as a line segment that joins the center to the boundary of a circle. The length of the radius remains the same from the center to any point on the circumference of the circle. The radius is half the length of the diameter. Let us learn more about the meaning of radius, the radius formula, and how to find the radius of a circle. 1. 2. 3. 4. 5. 6. 7. Radius of Circle Formulas The radius of a circle can be calculated using some specific formulas that depend on the known quantities and parameters. Radius Formula with Diameter The Radius = Diameter ÷ 2 Radius Formula from Circumference The The radius is the Radius = Circumference/2π Radius Formula using Area The 2. Here, r is the radius and π is the constant which is equal to 3.14159. The radius formula using the area of a circle is expressed as: Radius = √(Area/π) Radius of Circle Radius is an important part of a circle. It is the length between the center of the circle to any point on its boundary. In other words, when we connect the center of a circle to any point on its circumference using a straight line, that line segment is the radius of that particular circle. A circle can have multiple radii because there are infinite points on the circumference of a circle. This means that a circle has an infinite number of radii and all these radii are equidistant from the center of the circle. The size of the circle changes as soon as the length of the radius changes. In the figure given belo...

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Radius of a Circle Definition The circle is one of the most fundamental geometric shapes in mathematics, with a wide range of applications in various fields such as engineering, physics, architecture, and more. Understanding the properties of a circle, and in particular, its radius, is crucial in many areas of mathematics, from geometry to calculus. In this article, we will explore the definition of the radius of a circle in different branches of mathematics, including classical geometry, trigonometry, and analytical geometry. We will also discuss the applications of the radius of a circle in various fields and examine its properties and relationships with other geometric concepts. Definition of Radius in Classical Geometry Classical geometry is a branch of mathematics that deals with the properties of geometric shapes in two or three-dimensional space. In classical geometry, we define a circle as a set of points in a plane at an equal distance from a fixed point, known as the center of the circle. The radius is the distance from the center to any point on the circle. Thus, the radius is a crucial element of a circle's definition in classical geometry, as it determines the circle's size, shape, and position. The diameter of a circle, which is twice the length of the radius, is equally important, as it represents the distance across the circle through the center. The circumference of a circle, on the other hand, is the distance around the circle. The radius of a circle has ...

Here we have circle A where A T ‾ \overline A P . 13 = A P 13=AP 13 = A P Circles Circles are the set of all points a given distance from a point. This means a circle is not all the space inside it; it is the curved line around a point that closes in a space. A circle has a center, which is that point in the middle and provides the name of the circle. A circle can have a: • radius (the distance from the center to the circle) • chord (a line segment from the circle to another point on the circle without going through the center) • secant (a line passing through two points of the circle) • diameter (a chord passing through the center) • circumference (the distance around the circle itself. Here is a crop circle that shows the flattened crop, a center point, a radius, a secant, a chord, and a diameter: Tangent to a circle Notice that the diameter connects with the center point and two points on the circle. A chord and a secant connect only two points on the circle. A tangent connects with only one point on a circle. What is a tangent? A tangent is a line (or line segment) that intersects a circle at exactly one point. To do that, the tangent must also be at a right angle to a radius (or diameter) that intersects that same point. In our crop circle U, if we look carefully, we can see a tangent line off to the right, line segment FO. That would be the tiny trail the circle makers walked along to get to the spot in the field where they started forming their crop circle. Crop cir...

Circle A circle is easy to make: Draw a curve that is "radius" away from a central point. And so: All points are the same distance from the center. You Can Draw It Yourself Put a pin in a board, put a loop of string around it, and insert a pencil into the loop. Keep the string stretched and draw the circle! = 4.52 (to 2 decimals) Or, using the Diameter: A = ( π/4) × D 2 Area Compared to a Square A circle has about 80% of the area of a similar-width square. The actual value is ( π/4) = 0.785398... = 78.5398...% And something interesting for you to try: Names Because people have studied circles for thousands of years special names have come about. Nobody wants to say "that line that starts at one side of the circle, goes through the center and ends on the other side" when they can just say "Diameter". So here are the most common special names: Lines A line that "just touches" the circle as it passes by is called a Tangent. A line that cuts the circle at two points is called a Secant. A line segment that goes from one point to another on the circle's circumference is called a Chord. If it passes through the center it is called a Diameter. And a part of the circumference is called an

The general equation for a circle is $$x^2+y^2+2gx+2fy+c = 0,$$ where $h = -g$ and $k = -f$. The radius is then $r =\sqrt$. The book says: • If $g^2+f^2-c = 0$, then it's a point circle. • If $g^2+f^2-c > 0$, then it's a real circle. • If $g^2+f^2-c < 0$, then it's an unreal or imaginary circle. What does that mean? A real circle is exactly what you normally think of as a circle; it has a radius that is a real number (not imaginary). A point "circle" is just a point; it's a circle with a radius of zero (hence a degenerate circle). An imaginary circle is one in which the radius is the square root of a negative number—i.e., imaginary. $\begingroup$ Who is "we"? And surely, you needn't call me "sir." Anyway, a circle is a point if its radius is zero. This seems to violate intuition regarding what a circle is, but keep in mind that a circle is merely the set of points that are a fixed distance away from the center. If that fixed distance is zero, then that set of points is simply the center point itself. In the same way, a line segment of length zero is a single point, a square of side length zero is a single point, a sphere of radius zero is a single point, and so on. $\endgroup$ Short Answer A circle can be described by the equation $$ r^2 = (x-h)^2 + (y-k)^2 $$ where $r$ is the radius of the circle and $(h,k)$ is the center of the circle. • If $r^2 = 0$, then this equation has only one solution, the point $(h,k)$. Thus the equation describes a "point circle". • If $r^2 > 0$...

Properties of the Chord of a Circle Given below are a few important properties of the chords of a circle. • The perpendicular to a chord, drawn from the center of the circle, bisects the chord. • Chords of a circle, equidistant from the center of the circle are equal. • There is one and only one circle which passes through three collinear points. • When a chord of circle is drawn, it divides the circle into two regions, referred to as the segments of the circle: the major segment and the minor segment. • A chord when extended infinitely on both sides becomes a secant. Formula of Chord of Circle There are two basic formulas to find the length of the chord of a circle: • Chord length using 2− d 2). Let us see the proof and derivation of this formula. In the circle given below, 2 + d 2 = r 2, which further gives 1/2 of Chord length = √(r 2− d 2). Thus, chord length = 2 ×√(r 2− d 2) • Chord length using Theorems of Chord of a Circle The chord of a circle has a few theorems related to it. Theorem 1: The perpendicular to a chord, drawn from the center of the circle, bisects the chord. Observe the following circle to understand the theorem in which OP is the perpendicular bisector of chord AB and the chord gets bisected into AP and PB. This means AP = PB Theorem 2: Chords of a circle, equidistant from the center of the circle are equal. Observe the following circle to understand the theorem in which chord AB = chord CD, and they are equidistant from the center if PO = OQ. Theorem...

When we studied right triangles, we learned that for a given acute angle measure, the ratio opposite leg length hypotenuse length \dfrac hypotenuse length opposite leg length ​ start fraction, start text, o, p, p, o, s, i, t, e, space, l, e, g, space, l, e, n, g, t, h, end text, divided by, start text, h, y, p, o, t, e, n, u, s, e, space, l, e, n, g, t, h, end text, end fraction was always the same, no matter how big the right triangle was. We call that ratio the sine of the angle. Something very similar happens when we look at the ratio arc length radius length \dfrac radius length arc length ​ start fraction, start text, a, r, c, space, l, e, n, g, t, h, end text, divided by, start text, r, a, d, i, u, s, space, l, e, n, g, t, h, end text, end fraction in a sector with a given angle. For each claim below, try explaining the reason to yourself before looking at the explanation. Two circles. The circle on the left is labeled circle one. The circle on the right is labeled circle two. Circle one is smaller than circle two. In circle one, a radius length is labeled R one, and arc length is labeled L one. The central angle measure of the arc in circle one is theta. In circle two, a radius length is labeled R two, and arc length is labeled L two. The central angle measure of the arc in circle two is theta. The arc length in circle 1 is ℓ 1 = θ 360 ° ⋅ 2 π r 1 \redE ℓ 1 ​ = 3 6 0 ° θ ​ ⋅ 2 π r 1 ​ start color #bc2612, ell, start subscript, 1, end subscript, end color #bc2612, eq...