Cyclic Quadrilaterals Flashcards

A quadrilateral where all four vertices lie on the circumference of a circle.

The sum of the opposite angles in a cyclic quadrilateral is 180°.

The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.

The diagonals of a cyclic quadrilateral intersect at an angle that is supplementary to the angle between the opposite arcs.

A quadrilateral is cyclic if and only if the sum of its opposite angles is 180°.

The opposite angles subtend the same arc, and the angle at the centre is twice the angle at the circumference.

If a tangent is drawn to a circle at a vertex of a cyclic quadrilateral, the angle between the tangent and a side is equal to the opposite interior angle.

If a cyclic quadrilateral is inscribed in a semicircle, one of its angles is a right angle.

A quadrilateral is not cyclic if the sum of its opposite angles is not 180°.

Cyclic quadrilaterals can be found in designs like wheels, gears, and circular windows where four points lie on a circle.