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Ex 10.5, 9 - Two circles intersect at two points B and C - Ex 10.5

  1. Chapter 10 Class 9 Circles
  2. Serial order wise
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Ex 10.5, 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 is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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