Question

7. If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of
the quadrilateral, prove that it is a rectangle.
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Answer 1

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.