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Question -

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



Answer -

Let ABCD be a cyclicquadrilateral having diagonals BD and AC, intersecting each other at point O.

 (Consider BD as achord)

тИаBCD+ тИаBAD = 180┬░ (Cyclic quadrilateral)

тИаBCD= 180┬░ тИТ 90┬░ = 90┬░

 (Considering AC as achord)

тИаADC+ тИаABC = 180┬░ (Cyclic quadrilateral)

90┬░ + тИаABC= 180┬░

тИаABC= 90┬░

Eachinterior angle of a cyclic quadrilateral is of 90┬░. Hence, it is a rectangle.


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