How to find the radius of a circle

2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44

Lifehacker has collected nine ways to help you cope with geometric problems.

Choose a formula based on known quantities.

Through the area of a circle

1. Divide the area of the circle by pi.
2. Find the root of the result.

• R is the required radius of the circle.
• S is the area of the circle. Recall that a circle is a plane inside a circle.
• π (pi) is a constant equal to 3, 14.

Through the circumference

1. Multiply pi by two.
2. Divide the circumference by the result.

• R is the required radius of the circle.
• P is the circumference (perimeter of the circle).
• π (pi) is a constant equal to 3, 14.

Through the diameter of the circle

In case you forgot, the radius is half the diameter. So if the diameter is known, just divide it by two.

• R is the required radius of the circle.
• D - diameter.

Through the diagonal of the inscribed rectangle

The diagonal of a rectangle is the diameter of the circle in which it is inscribed. And the diameter, as we have already remembered, is twice the radius. Therefore, it is sufficient to divide the diagonal by two.

• R is the required radius of the circle.
• d is the diagonal of the inscribed rectangle. Recall that it divides the figure into two right-angled triangles and is their hypotenuse - the side opposite the right angle. Therefore, if the diagonal is unknown, it can be found through the adjacent sides of the rectangle using the Pythagorean theorem.
• a, b - sides of the inscribed rectangle.

Through the side of the described square

The side of the circumscribed square is equal to the diameter of the circle. And the diameter - we repeat - is equal to two radii. So divide the side of the square by two.

• r is the required radius of the circle.
• a - side of the described square.

Through the sides and area of the inscribed triangle

1. Multiply the three sides of the triangle.
2. Divide the result by the four areas of the triangle.

• R is the required radius of the circle.
• a, b, c - sides of the inscribed triangle.
• S is the area of the triangle.

Through the area and semi-perimeter of the described triangle

Divide the area of the described triangle by its half-perimeter.

• r is the required radius of the circle.
• S is the area of the triangle.
• p - half-perimeter of a triangle (equal to half of the sum of all sides).

Through the area of the sector and its central angle

1. Multiply the area of the sector by 360 degrees.
2. Divide the result by the product of pi and the center angle.
3. Find the root of the resulting number.

• R is the required radius of the circle.
• S - area of a sector of a circle.
• α is the central angle.
• π (pi) is a constant equal to 3, 14.

Through the side of an inscribed regular polygon

1. Divide 180 degrees by the number of sides of the polygon.
2. Find the sine of the resulting number.
3. Multiply the result by two.
4. Divide the side of the polygon by the result of all the previous steps.

• R is the required radius of the circle.
• a - side of a regular polygon. Recall that in a regular polygon, all sides are equal.
• N is the number of sides of the polygon. For example, if the problem has a pentagon like the image above, N would be 5.