MathematicsChoose the correct option:The radius of a circle is 10 cm and the length of one of its chords is 12 cm. Find the distance of the chord from the centre.

Choose the correct option:

The radius of a circle is 10 cm and the length of one of its chords is 12 cm. Find the distance of the chord from the centre.

  1. A

    6 cm

  2. B

    7 cm

  3. C

    8 cm

  4. D

    10 cm

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    Solution:

    Let AB be a chord of a circle with centre O and radius 10 cm such that AB = 12 cm.

    We draw OL ⊥ AB and join OA.


    Since the perpendicular from the centre of a circle to a chord bisects the chord.

    ∴ AL = LB = AB/2 = 6 cm

    Now in △OAL, we have

    OL2 = OA2 - AL2      [By Pythagoras theorem]

    ⇒ OL2 = (10)2 - (6)2

    ⇒ OL2 = 100 - 36 = 64

    ⇒ OL = 8 cm

    Hence the distance of the chord from the centre is 8 cm.

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