Tangential Quadrilateral Calculator

Calculations at a tangential quadrilateral. A tangential quadrilateral is a quadrilateral or quadrangle, whose sides are tangents, so they lie on a circle. So it has an incircle.
Enter three of the four sides a, b, c and d, and radius or area. Choose the number of decimal places and click Calculate.

	Side a:
	Side b:
	Side c:
	Side d:
	Radius (r):
	Area (A):
	Perimeter (p):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

Side lengths, radius and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

A tangent is a straight line that touches a curve at one point without the two intersecting. The tangent quadrilateral consists of four connected tangents of a circle. Tangent quadrilaterals also include the special cases of square, rhombus and kite. A trapezoid can also be a tangent quadrilateral, in which case it is a tangent trapezoid. If it does not belong to these special cases, then the tangent quadrilateral has no symmetries. The generalization of the tangent quadrilateral to any number of sides and corners is a tangent polygon. Only a triangle is always a tangent polygon; this does not apply to all other polygons of size n.
The formula for the connection between the sides, a + c = b + d, is Pitot's theorem, named after the French engineer Henri Pitot, who proved it in 1725. The area of ​​the tangent quadrilateral is the radius of the circumcircle multiplied by the sum of two opposite sides, regardless of which ones they are.
It is not possible to calculate the angles in the tangent quadrilateral from this information alone. If the two opposite angle added together are equal, i.e. both α+γ and β+γ are 180 degrees, then the tangent quadrilateral is also a cyclic quadrilateral and thus a cyclic tangent quadrilateral.