Prove that in a cyclic quadrilateral, sum of opposite sides is equal - Maths - Circles

Question

Prove that in a cyclic quadrilateral, sum of opposite sides is
equal

Anuradha Sharma · Accepted Answer

Since length of tangents drawn from an external point to a circle
are equal

DR=DS
CR=CQ

AP=AS

BP=BQ

Adding above 4 equations, we get

DR+CR+AP+BP
= DS+CQ+AS+BQ

( DR+CR 
) + ( AP+BP ) = ( DS+AS
) + ( CQ+BQ

)

DC+AB=DA+CB