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Prove that line from the center …

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Prove that line from the center of the circle to the chord bisects it

    • Posted by Devansh Mittal 3 years, 9 months ago

    CBSE > Class 09 > Mathematics
    • 2 answers

    Meenkashi Singh 3 years, 9 months ago

    To prove that the perpendicular from the centre to a chord bisect the chord. Consider a circle with centre at O and AB is a chord such that OXperpendicular to AB To prove that   AX=BX In ΔOAX and ΔOBX ∠OXA=∠OXB  [both are 90 ] OA=OB  (Both  are radius of circle ) OX=OX  (common side ) ΔOAX≅ΔOBX AX=BX  (by property of congruent triangles ) hence proved.

    0Thank You

    Gaurav Seth 3 years, 9 months ago

    • Prove that the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.

    Given :-

    • O is the center of circle
    • AB is chord of circle
    • OX bisects AB   i.e.   AX = BX

     

    To Prove :-

    • OX ⊥ AB

     

    Explanation :-

     

    ➠ In ∆AOX and ∆BOX,

     

     

     

     

    ➠ On line AB,

     

    Hence, ∠AXO and ∠BXO form a linear pair

     

     

     

    Hence, Proved.

     

    1Thank You

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