First, let us give a definition of radius. Translated from Latin, radius is “beam, wheel spoke”. The radius of a circle is a segment of a line connecting the center of a circle with a point located on it. The length of this segment is the value of the radius. In mathematical calculations, the Latin letter R is used to denote this value.
Tips for finding the radius:
- The diameter of a circle is a segment of a line passing through its center and connecting points lying on a circle that are as far apart as possible. The radius of the circle is equal to half its diameter, therefore, if you know the diameter of the circle, then to find its radius, apply the formula: R = D / 2, where D is the diameter.
- The length of the closed curve that forms on the plane is the circumference. If you know its length, then to find the radius of the circle, you can apply a universal formula of its kind: R = L / (2 * π), where L is the circumference and π is a constant equal to 3.14. The constant π is the ratio of the circumference of a circle to the length of its diameter; it is the same for all circles.
- A circle is a geometric figure that is part of a plane bounded by a curve - a circle. In that case, if you know the area of a circle, then the radius of the circle can be found using the special formula R = √ (S / π), where S is the area of the circle.
- The radius of the inscribed circle (squared) is as follows: r = a / 2, where a is the side of the square.
- The radius of the circumscribed circle (around the rectangle) is calculated by the formula: R = √ (a2 + b 2) / 2, where a and b are the sides of the rectangle.
- In the event that you do not know the length of the circle, but know the height and length of any of its segments, then the form of the formula will be as follows:
R = (4 * h2 + L2) / 8 * h, where h is the height of the segment and L is its length.
Find the radius of the circle inscribed in the triangle (rectangular). In a triangle, no matter how it looks, only one single circle can be inscribed, the center of which will be at the same time the point where the bisectors of its angles intersect. A right-angled triangle has many properties that must be considered when calculating the radius of an inscribed circle. Various data can be given in the problem; therefore, it is required to perform additional calculations necessary to solve it.
Tips for finding the radius of the inscribed circle:
- First you need to build a triangle with the dimensions that have already been set in your task. This must be done, knowing the dimensions of all three sides or two sides and the angle between them. Since the size of one corner is already known to you, then there should be two legs in the condition. The legs that are opposite the corners should be designated as a and b, and the hypotenuse as c. As for the radius of the inscribed circle, it is denoted as r.
- To apply the standard formula for determining the radius of an inscribed circle, you need to find all three sides of a right triangle. Knowing the dimensions of all sides, you can find the half-perimeter of a triangle from the formula: p = (a + b + c) / 2.
- If you know one corner and the leg, then you should determine whether it is adjacent or opposite. If it is adjacent, then the hypotenuse can be calculated using the cosine theorem: c = a / cosCBA. If it is opposite, then it is required to use the sine theorem: c = a / sinCAB.
- If you have a half-perimeter, then you can determine the radius of the inscribed circle. The form of the formula for the radius will be: r = √ (pb) (pa) (pc) / p.
- It should be noted that the radius can be found by the formula: r = S / p. So if you know two legs, then the calculation procedure will be easier. The hypotenuse required for a half-perimeter can be found by the sum of the squares of its legs. You can calculate the area by multiplying all available legs and dividing in two the number that you received.