Question 8:
A quadrilateral ABCD is drawn to circumscribe a circle (see given figure) Prove that AB + CD = AD + BC
Answer:
It can be observed that
DR = DS (Tangents on the circle from point D) … (1)
CR = CQ (Tangents on the circle from point C) … (2)
BP = BQ (Tangents on the circle from point B) … (3)
AP = AS (Tangents on the circle from point A) … (4)
Adding all these equations, we obtain
DR + CR + BP + AP = DS + CQ + BQ + AS
(DR + CR) + (BP + AP) = (DS + AS) + (CQ + BQ)
CD + AB = AD + BC
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