if a diagonals of cyclic quadrilateral are diameters of the circle to the vertisis of quadrilateral prove that if it is a rectangle
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Step-by-step explanation:
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.
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