Ex 10.4, 3 - If two equal chords of a circle intersect - Equal chords and their distance from centre

Ex 10.4, 3 - Chapter 10 Class 9 Circles - Part 2

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Ex10.4, 3 If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords. Given: Let AB & CD be the two equal chords intersecting at point X. ⇒ AB = CD To prove: OX makes equal angles with the chord i.e. ∠ OXA = ∠ OXD Proof: We draw OM ⊥ AB & ON ⊥ CD In ΔOMX and ΔONX, ∠OMX = ∠ONX OX = OX OM = ON ∴ ΔOMX ≅ ΔONX ΔOPX ≅ ΔOQX ∴ ∠OXM = ∠OXN i.e., ∠ OXA = ∠ OXD 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.