Two chords AB, CD of lengths 5 cm, 11 cm respectively of a circle are parallel. If the distance between AB and CD is 3 cm, find the rad

Question

Two chords AB, CD of lengths 5 cm, 11 cm respectively of a circle are parallel. If the
distance between AB and CD is 3 cm, find the radius of the circle.​

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Claire 3 weeks 2021-09-04T02:32:54+00:00 1 Answer 0 views 0

Answers ( )

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    2021-09-04T02:33:57+00:00

    Answer:

    r = 6.04 cm

    Step-by-step explanation:

    Given: AB = 11cm

    CD = 5cm

    AB ║ CD

    Draw OP ⊥ AB and OQ ⊥ CD

    PQ = 3cm

    To Find: Radius (r) of the circle.

    Sol: In triangle AOP

    AP = 1/2 AB (The perpendicular from the centre of the circle bisects the chord.)

    AP = 1/2 x11 = 5.5cm

    Let OP = x cm

    OA² = AP² + x²

    r² = (5.5)² + x²

    r² – (5.5)² = x²

    In ΔCOQ,

    CQ = 1/2 CD (theorem)

    CQ = 1/2 x 5 = 2.5

    OC² = CQ² + OQ²

    r² = (2.5)² + (x+3)²

    Now,

    (5.5)² + x² = (2.5)² + (x+3)²

    (5.5)² – (2.5)² = (x+3)² (x)²

    8×3 = (2x+3) (3)

    ∴2x + 3 = 8

    x = 5/2 = 2.5 cm

    Substituting x = 2.5

    r² = (5.5)² + (2.5)²

    r² = 36.5

    r = √36.5 = 6.04 cm

    *Hope it helps*

    *Kindly mark as brainliest*

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