10 Important Circle ⭕ Properties, Cyclic Quadrilateral

Two tangents PQ and PR are drawn from an external point to a circle with centre O . Prove that QORP is cyclic quadrilateral.

If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.

If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.

If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.

The area of a cyclic quadrilateral ABCD is (3sqrt3)/4 . The radius of the circle circumscribing cyclic quadrilateral is 1.If AB =1 and BD =sqrt3 , then BC*CD is equal to

Two tangents P Aa n dP B are drawn from an external point P to a circle with centre Odot Prove that A O B P is a cyclic quadrilateral.

In the adjoining figure, AB= AD, BD= CD and angleDBC= 2 angleABD Prove that : ABCD is a cyclic quadrilateral.

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle

The sum of either pair of opposite angles of a cyclic quadrilateral is 180^0 OR The opposite angles of a cyclic quadrilateral are supplementary.