Q. 44.0( 4 Votes )

Let us prove that for a quadrilateral circumscribed about a circle, the angles subtended by any two opposite sides at the centre are supplementary to each other.

Answer :


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Let us assume OAD = OAB = a


OBC = OBA = b


OCD = OCB = c


ODC = ODA = d


Since ABCD is a quadrilateral, so


2 (a + b + c + d) = 3600


a + b + c + d = 1800 …Equation (i)


In Δ AOB


AOB = 1800- (a + b)


In Δ COD


COD = 1800-(c + d)


AOB + COD = 3600–(a + b + c + d)


Putting the value from Equation (i) we get


AOB + COD = 3600–1800


AOB + COD = 1800


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