Tangential Quadrilateral
TangentialQuadrilateral
A quadrilateral which has an incircle, i.e., one for which a single circle can be constructed which is tangent to all four sides. Opposite sides of such a quadrilateral satisfy
| s=a+c=b+d, |
(1)
|
where
| s=1/2(a+b+c+d) |
(2)
|
is the semiperimeter, and the area is
| A=rs, |
(3)
|
where r is the inradius. Using Bretschneider's formula together with (1) and (3) then gives the beautiful formula
where p and q are the diagonal lengths.
A rhombus is a special case of a tangential quadrilateral.
See also
Bicentric Quadrilateral, Cyclic Quadrilateral, Incircle, Quadrilateral, Rhombus, Tangential TriangleExplore with Wolfram|Alpha
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References
Harris, J. W. and Stocker, H. "Quadrilateral of Tangents." §3.6.8 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, p. 86, 1998.Referenced on Wolfram|Alpha
Tangential QuadrilateralCite this as:
Weisstein, Eric W. "Tangential Quadrilateral." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TangentialQuadrilateral.html