Ex 10.4, 2 - If two equal chords of a circle intersect - Equal chords and their distance from centre

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

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Transcript

Ex 9.2, 2 If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord. Given: Let AB & CD be the two equal chords intersecting at point X. ⇒ AB = CD To prove: Corresponding segments are equal, i.e., AX = DX and BX = CX Proof: We draw OM ⊥ AB & ON ⊥ CD So, AM = BM = 1/2 AB & DN = CN = 1/2 CD As AB = CD, ⇒ 1/2 AB = 1/2 CD ∴ AM = DN & MB = CN In ΔOMX and ΔONX, ∠OMX = ∠ONX OX = OX OM = ON ∴ ΔOMX ≅ ΔONX ∴ MX = NX Adding (1) & (3) AM + MX = DN + NX AX = DX Therefore, AX = DX & BX = CX 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.