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Chords equidistant from the center of a ...

Chords equidistant from the center of a circle are equal in length.

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In `/_\AOX` and `/_\DOY`
`/_OXA=/_OYD` (perpendicular angles)
`OA=OD` (radius)
`OX=OY` (given)
By RHS congruency, `/_\AOX` and `/_\DOY` are congreunt.
`AX=DY` (CPCT)
For chord `AB`
...
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Knowledge Check

  • r : Two chords of a circle are equidistant from the centre if and only if they are equal in length Statements r can be interpreted as

    A
    If two polygons are congruent then they are equal in shape and size
    B
    If two polygons are equal in shape and size then· they' are not congruent
    C
    Both (1) & (2)
    D
    Noen of these

  • Calculate the angle subtended by the chord at the point on the major arc if the radius and the chord of the circle are equal in length

    A
    A) `30^@`
    B
    B) `120^@`
    C
    C) `200^@`
    D
    D) `300^@`

  • If a chord of length 16 cm is at a distance of 15 cm from the centre of the circle, then the length of the chord of the same circle which is at a distance of 8 cm from the centre is equal to

    A
    10 cm
    B
    20 cm
    C
    30 cm
    D
    40 cm

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    Write the following statements in conditional form, "chords, which are equidistant from the centers of congruent circles, are congruent."

    Chord AB is 6 inches from the center of the circle and is 10 inches long.Draw another chord CD that is equidistant from the center of the circle.How long is chord CD?

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