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
(1)
where
(2)
is the semiperimeter , and the area
is
(3)
where
is the inradius . Using Bretschneider's
formula together with (1 ) and (3 ) then
gives the beautiful formula
where
and
are the diagonal lengths.
A rhombus is a special case of a tangential quadrilateral.
See also Bicentric Quadrilateral ,
Cyclic Quadrilateral ,
Incircle ,
Quadrilateral ,
Rhombus ,
Tangential Triangle
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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 Quadrilateral
Cite this as:
Weisstein, Eric W. "Tangential Quadrilateral."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/TangentialQuadrilateral.html
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