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20/06/2021 10:51 am
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A quadrilateral ABCD is drawn to circumscribe a circle (see Fig.). Prove that AB + CD = AD + BC
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20/06/2021 10:59 am
From this figure we can conclude a few points which are:
(i) DR = DS
(ii) BP = BQ
(iii) AP = AS
(iv) CR = CQ
Since they are tangents on the circle from points D, B, A, and C respectively.
Now, adding the LHS and RHS of the above equations we get,
DR + BP + AP + CR = DS + BQ + AS + CQ
By rearranging them we get,
(DR + CR) + (BP + AP) = (CQ + BQ) + (DS + AS)
By simplifying,
AD + BC = CD + AB