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Ex 10.2, 8 - A quadrilateral ABCD is drawn to circumscribe - Ex 10.2

Ex 10.2, 8 - Chapter 10 Class 10 Circles - Part 2

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Ex 10.2,8 A quadrilateral ABCD is drawn to circumscribe a circle (see figure). Prove that AB + CD = AD + BC Given : Let ABCD be the quadrilateral circumscribing the circle with centre O. The quadrilateral touches the circle at points P,Q,R and S To prove: AB + CD = AD + BC Proof: From theorem 10.2, lengths of tangents drawn from external point are equal Hence, AP = AS BP = BQ CR = CQ DR = DS Adding (1) + (2) + (3) + (4) AP + BP + CR + DR = AS + BQ + CQ + DS (AP + BP) + (CR + DR )= (AS + DS ) + (BQ + CQ) AB + CD = AD + BC Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.