Question

Which of the following are true about cyclic quadrilaterals?

• A. The sum of the opposite angles of a cyclic quadrilateral is supplementary.
• B. If two opposite angles of a quadrilateral are supplementary, then it is a cyclic quadrilateral.
• C. Perpendicular Bisectors of a quadrilateral are concurrent only if it is a cyclic quadrialateral.
• D. The four perpendicular bisectors of the four sides meet at the centre of the circle only if it is a cyclic quadrilateral.

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A The sum of the opposite angles of a cyclic quadrilateral is supplementary.
B If two opposite angles of a quadrilateral are supplementary, then it is a cyclic quadrilateral.
C Perpendicular Bisectors of a quadrilateral are concurrent only if it is a cyclic quadrialateral.
D The four perpendicular bisectors of the four sides meet at the centre of the circle only if it is a cyclic quadrilateral.

The properties of a cyclic quadrilateral are:
If one side of the cyclic quadrilateral is produced, then the exterior angle so formed is equal to the interior opposite angle.
The sum of the opposite angles of a cyclic quadrilateral is supplementary.
If two opposite angles of a quadrilateral are supplementary, then it is a cyclic quadrilateral.
In a cyclic quadrilateral, the ratio of the diagonals equals the ratio of the sum of products of the sides that share the diagonal's endpoints.
Perpendicular Bisectors of a quadrilateral are concurrent only if it is a cyclic quadrialateral.
The four perpendicular bisectors of the four sides meet at the centre of the circle only if it is a cyclic quadrilateral.
According to cyclic quadrilateral conjecture, the opposite angles of a cyclic quadrilateral are supplementary.