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

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  1. Chapter 10 Class 9 Circles
  2. Serial order wise
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Transcript

Ex 10.4, 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 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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