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Question -

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



Answer -

Let ABCD be a cyclicquadrilateral having diagonals BD and AC, intersecting each other at point O.

 (Consider BD as achord)

∠BCD+ ∠BAD = 180° (Cyclic quadrilateral)

∠BCD= 180° − 90° = 90°

 (Considering AC as achord)

∠ADC+ ∠ABC = 180° (Cyclic quadrilateral)

90° + ∠ABC= 180°

∠ABC= 90°

Eachinterior angle of a cyclic quadrilateral is of 90°. Hence, it is a rectangle.


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