# 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.

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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