12 Facts About Cyclic quadrilateral

An example of a quadrilateral that cannot be cyclic is a non-square rhombus.

Convex quadrilateral is cyclic if and only if the four perpendicular bisectors to the sides are concurrent.

Convex quadrilateral is cyclic if and only if its opposite angles are supplementary, that is.

Equivalently, a convex quadrilateral is cyclic if and only if each exterior angle is equal to the opposite interior angle.

Convex quadrilateral is cyclic if and only if an angle between a side and a diagonal is equal to the angle between the opposite side and the other diagonal.

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If, the cyclic quadrilateral becomes a triangle and the formula is reduced to Heron's formula.

Cyclic quadrilateral has maximal area among all quadrilaterals having the same side lengths .

Where there is equality if and only if the Cyclic quadrilateral is a square.

Four line segments, each perpendicular to one side of a cyclic quadrilateral and passing through the opposite side's midpoint, are concurrent.

Brahmagupta quadrilateral is a cyclic quadrilateral with integer sides, integer diagonals, and integer area.

In spherical geometry, a spherical quadrilateral formed from four intersecting greater circles is cyclic if and only if the summations of the opposite angles are equal, i e, a + ? = ß + d for consecutive angles a, ß, ?, d of the quadrilateral.

Lexell showed that in a spherical Cyclic quadrilateral inscribed in a small circle of a sphere the sums of opposite angles are equal, and that in the circumscribed Cyclic quadrilateral the sums of opposite sides are equal.