Conditions For A Tangential Quadrilateral To Be Another Type of Quadrilateral
A tangential quadrilateral is a rhombus if and only if its opposite angles are equal.
If the incircle is tangent to the sides AB, BC, CD, DA at W, X, Y, Z respectively, then a tangential quadrilateral ABCD is also cyclic (and hence bicentric) if and only if any of
- WY is perpendicular to XZ
The first of these three means that the contact quadrilateral WXYZ is an orthodiagonal quadrilateral.
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
- 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 the diagonal that is the axis of symmetry.
Read more about this topic: Tangential Quadrilateral
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