two circles of radii 5cm and 3cm intersect at two points and the distance between their centres is 4 cm find the length of the common chord​

Question

two circles of radii 5cm and 3cm intersect at two points and the distance between their centres is 4 cm find the length of the common chord​

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Athena 1 month 2021-08-20T10:17:01+00:00 1 Answer 0 views 0

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    2021-08-20T10:18:08+00:00

    Answer:

    Let the common chord be AB and P and Q be the centers of the two circles.

    ∴AP=5cm and AQ=3cm.

    PQ=4cm ….given

    Now, segPQ⊥chord AB

    ∴AR=RB=

    2

    1

    AB ….perpendicular from center to the chord, bisects the chord

    Let PR=xcm, so RQ=(4−x)cm

    In △ARP,

    AP

    2

    =AR

    2

    +PR

    2

    AR

    2

    =5

    2

    −x

    2

    …(1)

    In △ARQ,

    AQ

    2

    =AR

    2

    +QR

    2

    AR

    2

    =3

    2

    −(4−x)

    2

    …(2)

    ∴5

    2

    −x

    2

    =3

    2

    −(4−x)

    2

    ….from (1) & (2)

    25−x

    2

    =9−(16−8x+x

    2

    )

    25−x

    2

    =−7+8x−x

    2

    32=8x

    ∴x=4

    Substitute in eq(1) we get,

    AR

    2

    =25−16=9

    ∴AR=3cm.

    ∴AB=2×AR=2×3

    ∴AB=6cm.

    So, length of common chord AB is6cm

    Step-by-step explanation:

    plz

    Mark As Branliest

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