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prove that OM bisect AB .IF OM …

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prove that OM bisect AB .IF OM  PERPENDICULAR AB

 

    • Posted by Harsh Agrawal 8 years, 10 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Shweta Gulati 8 years, 10 months ago

    The perpendicular from the centre to the chord bisects the chord

    In the diagram below, AB is the chord of a circle with centre O.

    OM is the perpendicular from the centre to the chord.

     

    Look at triangles OAM and OBM.

    The hypotenuses (OA and OB) are the same, as they are both the radius of the circle.

    OM is common to both triangles.

    OMA and OMB are both right angles.

    Triangles OAM and OBM are congruent (RHS), so it follows that AM = MB.

    Therefore, M is the midpoint of AB, and the chord has been bisected.

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