Kite (geometry) - Conditions For When A Tangential Quadrilateral Is A Kite

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

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