Answer :


Property: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal.


By the above property,


AP = AS (tangent from A)


BP = BQ (tangent from B)


CR = CQ (tangent from C)


DR = DS (tangent from D)


Now we add above 4 equations,


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


AB + CD = AD + BC


[ AP + BP = AB


CR + DR = CD


AS + DS = AD


BQ + CQ = BC]


Hence, proved


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