Ex 10.6, 1 (Optional) - Prove that line of centers of two intersecting

Ex 10.6, 1 (Optional) - Chapter 10 Class 9 Circles - Part 2

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Question 1 Prove that the line of centers of two intersecting circles subtends equal angles at the two points of intersection. Given: Two intersecting circles where PQ is the line joining the centers and A, B are the points of intersection To Prove: PQ subtends equal angles at A & B i.e. ∠PAQ = ∠PBQ Construction: Join PA, PB, QA & QB Proof: In ∆PAQ & PBQ, PA = PB QA = QB PQ = PQ ∆ PAQ ≅ ∆ PBQ ∴ PAQ = ∠PBQ Hence Proved (Radii of the same circle) (Radii of the same circle) (Common Side) (SSS Congruency Rule) (By CPCT)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.