If diagonal of a cyclic qu
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Gaurav Seth 3 years, 5 months 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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