Conditions For When A Tangential Quadrilateral Is A Kite
A tangential quadrilateral is a kite if and only if any one of the following conditions is true:
- The area is one half the product of the diagonals.
- The diagonals are perpendicular. (Thus the kites are exactly the quadrilaterals that are both tangential and orthodiagonal.)
- The two line segments connecting opposite points of tangency have equal length.
- One pair of opposite tangent lengths have equal length.
- The bimedians have equal length.
- The products of opposite sides are equal.
- The center of the incircle lies on a line of symmetry that is also a diagonal.
If the diagonals in a tangential quadrilateral ABCD intersect at P, and the incircles in triangles ABP, BCP, CDP, DAP have radii r1, r2, r3, and r4 respectively, then the quadrilateral is a kite if and only if
If the excircles to the same four triangles opposite the vertex P have radii R1, R2, R3, and R4 respectively, then the quadrilateral is a kite if and only if
Read more about this topic: Kite (geometry)
Famous quotes containing the words conditions, tangential and/or kite:
“The depth and strength of a human character are defined by its moral reserves. People reveal themselves completely only when they are thrown out of the customary conditions of their life, for only then do they have to fall back on their reserves.”
—Leon Trotsky (1879–1940)
“New York is full of people ... with a feeling for the tangential adventure, the risky adventure, the interlude that’s not likely to end in any double-ring ceremony.”
—Joan Didion (b. 1934)
“A saint about to fall,
The stained flats of heaven hit and razed
To the kissed kite hems of his shawl....”
—Dylan Thomas (1914–1953)