Rectangle Circumcircle

Find the circumscribed circle radius of a rectangle from its height and width, plus the diagonal, circle area, and diameter.

Input

Enter the height and width of a rectangle to find the radius of the circle passing through its four corners.

Height a

Width b

Circumcircle radius R

Diagonal

Circle area

78.539816

Diameter

Circumference

31.415927

Rectangle area

Lengths use the same unit as your input, and areas use the square of that unit.

The four corners of a rectangle all lie on one circle, called the circumscribed circle. Its center is exactly where the two diagonals cross.
The diameter of the circumscribed circle equals the rectangle diagonal. With height a and width b, the diagonal is the square root of (a squared plus b squared) by the Pythagorean theorem.
The circumradius R is half of the diagonal, so R equals the square root of (a squared plus b squared) divided by 2.
The circle area is pi times R squared and the circumference is 2 times pi times R. The rectangle area is a times b.
Lengths are shown in the same unit as your input. Areas use the square of that unit.

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