The radius of the circle

To begin, let us define a radius. Translated from the Latin radius – “ray, spoke of wheel”. The radius of the circle – a line segment connecting the center of the circle with the dot that is on it. The length of this segment – is the value of the radius. In mathematical calculations to refer to that value use 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 lying on the circumference, which are most removed from each other. The radius of the circle is equal to half its diameter, therefore, if you know the diameter of a circle, then its radius should use the formula: R = D/2 where D  – diameter.
2. The length of the closed curve formed on a plane – the length of the circumference. If you know its length, for finding the radius of a circle you can apply a universal a-kind formula: R = L/(2*π), where L is the length of the circumference, and π – a constant equal 3,14. The constant π is the ratio of the circumference to the length of its diameter, it is the same for all circles.
3. The Circle is a geometric figure that is part of a plane bounded curve-a circle. In that case, if you know the area of any circle, the radius of the circle can be found using a special formula R = √(S/π), where S is the area of a circle.
4. Vpisano the Radius of the circle (square) is as follows: r = a/2 where a is side of the square.
5. The Radius of the circumscribed circle (around the rectangle) is calculated according to the formula: R = √ (a2 + b 2)/2, where a and b are the sides of the rectangle.
6. If you don't know the circumference, but I know the height and the length of any segment, the formula would be:

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

Find the radius of a circle inscribed in a triangle (right angle). In a triangle, whatever he had, it can be entered in only one single circumference, the center of which is simultaneously the point where the bisectors of its angles. A right triangle has many properties that must be taken into account when computing the radius of the inscribed circle. The task can be given different data, hence the need to perform additional calculations needed to solve it.

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Tips for finding the radius of the inscribed circle:

1. First you need to build a triangle with those dimensions that were specified in your task. This must be done, knowing the sizes of all three sides or two sides and angle between them. As the size of one angle is already known, then the condition needs to be two sides. The legs, which protivorechat the corners must be designated as a and b, and the hypotenuse is – like C. as for the inradius, then it is denoted as r.
2. To apply the standard formula for determining the radius of the inscribed circle is required to find all three sides of a right triangle. Knowing the dimensions you'll be able to find properiter triangle from the formula: p = (a + b+ c)/2.
3. If you know one angle and side, you need to determine the adjacent or opposite it. If it is adjacent, the hypotenuse can be calculated using the theorem of cosines: c = a/cosCBA. If it is opposite, then you need to use the theorem of sines: c=a/sinCAB.
4. If you have pauperised, you can determine the radius of the inscribed circle. The formula for radius is: r=√(p-b)(p-a)(p-c)/p.
5. It Should be noted that to find the radius by the formula: r = S/p. So if you know two sides, then the calculation procedure will be easier. The hypotenuse required to properiety, can be found by the sum of the squares of its other two sides. Calculate the area you can multiply all the sides, and dividing into two the number that you received.