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Drishya
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Asked: 2020-11-05T09:52:27+00:00 In:

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.

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NCERT Solutions for Class 9 Maths Chapter 10
Important NCERT Questions
Circles
NCERT Books for Session 2022-2023
CBSE Board, UP Board and Other state Boards
EXERCISE 10.4
Page No:179
Questions No:3

2020-2021cbsechapter 10circlesclass 9mathematicsncert
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    2 Answers

    1. Get Hindi Medium and English Medium NCERT Solution for Class 9 Maths to download.
      Please follow the link to visit website for first and second term exams solutions.
      https://www.tiwariacademy.com/ncert-solutions/class-9/maths/chapter-10/

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    2. Best Answer
      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 : In circle C (O, r) equal chords AB and CD intersects at point P.
      To Prove: ∠OPM = ∠OPN
      Construction: Join OP. Draw OM ⊥ AB and ON ⊥CD.
      Proof: In ΔOMP and ΔONP,
      ∠OMP = ∠ONP [∵ Each 90°]
      AP = AP [∵ Common]
      OM = ON [∵ Equal chords of a circle are equidistant from the centre]
      Hence, ΔOMP ≅ ΔONP [∵ RHS Congruency rule]
      ∠OPM = ∠OPM [∵ CPCT]

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