If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral,prove that it is a rectangle. -Maths 9th

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral,prove that it is a rectangle. -Maths 9th
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Solution :- Let, ABCD be a cyclic quadrilateral such that its diagonal AC and BD are the diameters of the circle though the vertices A,B,C and D. As angle in a semi-circle is 900 ∴  ∠ABC = 900 and ∠ADC = 900     ∠DAB = 900  and ∠BCD = 900                                                                          So,     ∠ABC = ∠BCD = ∠CDA = ∠DAB = 900                                                       Hence, ABCD is a rectangle.
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