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| 1. |
If diagonal of a cyclic qu |
| Answer» 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.AnswerHere, ABCD is a cyclic quadrilateral in which AC and BD are diameters .Since AC is a diameter.∴ ∠ABC =\xa0∠ADC = 90°[∵ angle of a semicircle = 90°]Also, BD is a diameter\xa0∴∠BAD =\xa0∠BCD\xa0= 90°[∵ angle of a semicircle\xa0= 90°]Now, all the angles of a cyclic quadrilateral ABCD are\xa090° each. Hence, ABCD is a rectangle. | |