The radius of the circle

To begin with we define the radius.Translated from the Latin radius - this "ray spoke wheels."The radius of the circle - a line segment connecting the center of the circle with a point that is on it.The length of this segment - is the radius.In mathematical calculations to describe this value using the Latin letter R.

Tips for finding the radius:

  1. diameter of a circle is a line segment passing through its center and connecting points on the circumference of which a maximum distance from each other.The circle radius is equal to half its diameter, therefore, if you know the diameter of the circle, then to find its radius should apply the formula: R = D / 2 where D - diameter.
  2. Length closed curve, which is formed in a plane - this circumference.If you know its length, then to find the radius of a circle, you can apply the universal-a-kind formula: R = L / (2 * π), where L is the length of the circle, and π - constant equal to 3.14.Constant π represents the ratio of the circumference to its diameter,
    length, it is the same for all the circumferences.
  3. circle is a geometric figure, which is part of the plane bounded by the curve - circle.In that case, if you know the area of ​​a circle, the radius of the circle can be found by a special formula R = √ (S / π), where S is the area of ​​a circle.
  4. inscribing circle radius (in the square) is as follows: r = a / 2, where a is the side of the square.
  5. radius of the circle (around the rectangle) is calculated by the formula: R = √ (a2 + b 2) / 2, where a and b are the sides of the rectangle.
  6. In that case, if you do not know the length of the circle, but you know the height and the length of any of its segment, the type of formula will be as follows:

R = (4 * h2 + L2) / 8 * h, where h isheight segment, and L is its length.

find the radius of a circle inscribed in the triangle (rectangle).In a triangle, whatever kind he had not inscribed can be only one single circle whose center is at the same time the point at which intersect the bisector of its corners.A right triangle has a set of properties that must be taken into account when computing the radius of the inscribed circle.The task can be given a variety of data, therefore, is required to perform additional calculations required to solve it.

Tips for finding the radius of the inscribed circle:

  1. First you need to construct a triangle with the dimensions of which have already been given the task in hand.This should be done by knowing the size of all three sides or two sides and the angle between them.Since the size of one corner you are already known, it must be provided in the two leg.Legs of which are opposite corners must be designated as a and b, and the hypotenuse - both.With regard to the radius of the inscribed circle, it is designated as r.
  2. to use the standard formula for determining the radius of the inscribed circle is required to find all the three sides of a right triangle.Knowing the size of all the sides, you'll find semiperimeter triangle from the formula: p = (a + b + c) / 2.
  3. If you know of one corner and a leg, then you should define it or adjacent opposite.If it is adjacent, the hypotenuse can be calculated using the cosine theorem: c = a / cosCBA.If it is opposite, then you want to take advantage of the sine theorem: c = a / sinCAB.
  4. If you have semiperimeter, you can determine the radius of the inscribed circle.Type the formula for the radius will thus: r = √ (pb) (pa) (pc) / p.
  5. should be noted that the radius can be found by the formula: S = r / p.So if you know of leg two, the calculation procedure will be lighter.Hypotenuse required to semiperimeter can be found on the sum of the squares of the other two sides.Calculate the area, you can, all the legs of multiplying and dividing in half the number that you received.