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If diagonal of a cyclic qu

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If diagonal of a cyclic qu

Posted by Mohammed Basil 5 years ago

CBSE > Class 09 > Mathematics

1 answers

Gaurav Seth 5 years ago

If the diagonals of a cyclic quadrilateral are diameters of the circle through the opposite vertices of the quadrilateral. Prove that the quadrilateral is a rectangle.

Answer

Here, ABCD is a cyclic quadrilateral in which AC and BD are diameters .

Since AC is a diameter.

∴ ∠ABC = ∠ADC = 90°

[∵ angle of a semicircle = 90°]

Also, BD is a diameter

∴∠BAD = ∠BCD = 90°

[∵ angle of a semicircle = 90°]

Now, all the angles of a cyclic quadrilateral ABCD are 90° each.

Hence, ABCD is a rectangle.

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