# How to find the radius of a circle: to help students

How to find the radius of the circle?This question is always relevant for students studying planimetry.Below we look at some examples of how you can cope with this task.

Depending on the conditions of the problem circle radius you can find a way.

Formula 1: R = h / 2π, where h - is the length of the circle, and π - constant equal to 3,141 ...

Formula 2: R = √ (S / π), where S - the area is the size of the circle.

Formula 3: R = D / 2, where D - is the diameter of the circle, that is, the length of the segment that passes through the center of the figure, connects the two most distant points of each other.

How to find the radius of the circle

First, let's define the term itself.The circle described is called when it applies to all the vertices of the polygon.It should be noted that it is possible only to describe a circle around such a polygon whose sides and angles are equal to each other, that is, around an equilateral triangle, square, rhombus, etc. correctTo solve this problem you need to fi

nd the perimeter of a polygon, and died out of his hand and the area.So arm yourself with a ruler, compass, calculator, and a notebook with a pen.

How to find the radius of a circle if it is described around the triangle

Formula 1: R = (A * B * B) / 4S, where A, B, C - the length of the sides of the triangle and S - its area.

Formula 2: R = A / sin a, where A - the length of one side of the figure, and sin a - a calculated value of the sine of the opposite side of the angle.

radius of the circle, which is described around a rectangular triangle.

Formula 1: R = B / 2, where B - hypotenuse.

Formula 2: R = M * B, where B - the hypotenuse, and M - the median drawn to her.

How to find the radius of a circle when it is described around a regular polygon

formula: R = A / (2 * sin (360 / (2 * n))), where A - the length of one side of the figure, and n - number of sidesin a given geometric shape.

How to find the radius of the inscribed circle inscribed circle

called when it applies to all sides of the polygon.Consider a few examples.

Formula 1: R = S / (P / 2) wherein - R and S - area and perimeter shapes respectively.

Formula 2: R = (P / 2 - A) * tg (a / 2), where P - perimeter, and - the length of one of the parties, and - the angle opposite this side.

How to find the radius of a circle if it is inscribed in a right triangle

Formula 1:

radius of the circle, which is inscribed in a rhombus

circumference can be entered in any diamond as an equilateral and scalene.

Formula 1: R = 2 * N, where N - is the height of a geometric figure.

Formula 2: R = S / (A * 2), where S - is the area of ​​the rhombus, and A - is the length of its sides.

Formula 3: R = √ ((S * sin A) / 4) where S - is the area of ​​the rhombus, and A sin - acute angle to the sine of the geometrical figure.

Formula 4: R = H * D / (√ (V² + G²) where B and T - is the diagonal length of a geometric figure.

Formula 5: R = V * sin (A / 2), where - the diagonalrhombus, and A - is the angle at the vertices that connect the diagonal.

radius circle which is inscribed in the triangle

In the case in the problem you are the lengths of the sides of the figure, first calculate the perimeter of the triangle (D), thensemiperimeter (n):

C = A + B + C, where A, B, C - lengths of the sides of a geometric figure.

n = n / 2.

Formula 1: R = √ ((p-A) *(p-B) * (n-C) / n).

And if knowing all the same three sides, you have been given more and the area figure, you can calculate the required radius follows.

Formula 2: R = S2 * (A + B + C)

Formula 3: R = S / n = S / (A + B + C) / 2), where - n - is semiperimeter geometry.

Formula 4: R = (n - k) tg * (A / 2), where n - is semiperimeter triangle, and - one of its sides, and tg (A / 2) - tangent of half this side of the opposite corner.

A below, this formula will help to find the radius of the circle, which is inscribed in an equilateral triangle.

formula 5: R = A * √3 / 6.

radius of the circle, which is inscribed in a right triangle

If the problem given the length of the legs and the hypotenuse, the radius of the inscribed circle learned so.

Formula 1: R = (A + B-C) ​​/ 2, where A, B - catheti C - hypotenuse.

In that case, if you are only two leg, it's time to recall the Pythagorean Theorem to find the hypotenuse and to use the above formula.

C = √ (A² + B²).

radius of the circle, which is inscribed in a square

circle that is inscribed in a square, divided all of his 4 side exactly half the points of tangency.

Formula 1: R = A / 2, where A - the square side length.

Formula 2: R = S / (P / 2), where S and F - the area and perimeter of a square, respectively.

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