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A kite with three 108° angles and one 36° angle forms the convex hull of the lute of Pythagoras, a fractal made of nested pentagrams. [22] The four sides of this kite lie on four of the sides of a regular pentagon, with a golden triangle glued onto the fifth side. [16] Part of an aperiodic tiling with prototiles made from eight kites
If the incircle is tangent to the sides AB, BC, CD, DA at T 1, T 2, T 3, T 4 respectively, and if N 1, N 2, N 3, N 4 are the isotomic conjugates of these points with respect to the corresponding sides (that is, AT 1 = BN 1 and so on), then the Nagel point of the tangential quadrilateral is defined as the intersection of the lines N 1 N 3 and N ...
Kite: two pairs of adjacent sides are of equal length. This implies that one diagonal divides the kite into congruent triangles, and so the angles between the two pairs of equal sides are equal in measure. It also implies that the diagonals are perpendicular.
A right kite with its circumcircle and incircle. The leftmost and rightmost vertices have right angles. In Euclidean geometry, a right kite is a kite (a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other) that can be inscribed in a circle. [1]
In a deltoidal icositetrahedron, each face is a kite-shaped quadrilateral. The side lengths of these kites can be expressed in the ratio 0.7731900694928638:1 Specifically, the side adjacent to the obtuse angle has a length of approximately 0.707106785, while the side adjacent to the acute angle has a length of approximately 0.914213565.
Any square, rectangle, isosceles trapezoid, or antiparallelogram is cyclic. A kite is cyclic if and only if it has two right angles – a right kite.A bicentric quadrilateral is a cyclic quadrilateral that is also tangential and an ex-bicentric quadrilateral is a cyclic quadrilateral that is also ex-tangential.
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This formula cannot be used if the quadrilateral is a right kite, since the denominator is zero in that case. If M, N are the midpoints of the diagonals, and E, F are the intersection points of the extensions of opposite sides, then the area of a bicentric quadrilateral is given by