Question

The Converse of Ptolemy's theorem is

• A. If a quadrilateral is inscribable in a circle then the product of the measures of its diagonals is equal to the sum of the products of the measures of the pairs of opposite sides.
• B. In a quadrilateral, if the sum of the products of its two pairs of opposite sides is equal to the product of its diagonals, then the quadrilateral can be inscribed in a circle.
• C. Converse of the Ptolemy's theorem does not exist
• D. None of these

Answer 1

The correct option is B In a quadrilateral, if the sum of the products of its two pairs of opposite sides is equal to the product of its diagonals, then the quadrilateral can be inscribed in a circle.

According to Ptolemy's theorem in a cyclic quadrilateral the product of diagonals is equal to the sum of products of the lengths of opposite sides.

So its converse is :In a quadrilateral, if the sum of the products of its two pairs of opposite sides is equal to the product of its diagonals, then the quadrilateral can be inscribed in a circle

So option $B$ is correct.