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Ex 9.3, 9 Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see the given figure). Prove that ACP = QCD. Given: Two circles intersecting at B & C, line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively To prove: ACP = QCD i.e. 1 = 2 Construction: Join AP & DQ Let ABP = 3 & QBD = 4 Proof: For chord AP, 1 & 3 lie on the same segment ACBPA 1 = 3 Now, lines ABD & PBQ intersect at B 3 = 4 From (1), (2) & (3) 1 = 2 i.e. ACP = QCD Hence proved

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo