Question

If the diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of
the quadrilatual. Prove that it is a rectangle.
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Answer 1

Answer:

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

(Consider BD as a chord)

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

∠BCD = 180° − 90° = 90°

(Considering AC as a chord)

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

90° + ∠ABC = 180°

∠ABC = 90°

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