Plane Geometry


  1. In a circle of radius 21 cm, an arc subtends an angle of 72° at the centre. The length of the arc is









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    Here , Rradius ( r ) = 21 cm

    θ = 72° = 72 ×
    π
    radians
    180

    θ =
    radians
    5

    As we know that ,
    ∴ θ =
    l
    r

    l → length of arc
    ⇒ l = θ.r =
    × 21
    5

    Correct Option: B

    Here , Rradius ( r ) = 21 cm

    θ = 72° = 72 ×
    π
    radians
    180

    θ =
    radians
    5

    As we know that ,
    ∴ θ =
    l
    r

    l → length of arc
    ⇒ l = θ.r =
    × 21
    5

    l =
    2
    ×
    22
    × 21
    57

    l =
    132
    = 26.4 cm.
    5


  1. The distance between two parallel chords of length 8 cm each in a circle of diameter 10 cm is









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    As per the given in question , we draw a figure circle

    Given , Diameter = 10 cm
    AB = CD
    OP = OQ
    From ∆ OAP,
    OP = √OA² - AP²
    OP = √5² - 4²
    OP = √25 - 16

    Correct Option: A

    As per the given in question , we draw a figure circle

    Given , Diameter = 10 cm
    AB = CD
    OP = OQ
    From ∆ OAP,
    OP = √OA² - AP²
    OP = √5² - 4²
    OP = √25 - 16
    OP = √9 = 3 cm.
    ∴ QP = 2 × OP = 6 cm.



  1. The length of two chords AB and AC of a circle are 8 cm and 6 cm and ∠BAC = 90°, then the radius of circle is









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    According to question , we draw a figure of a circle with two chords AB and AC ,

    Here , AB = 8 cm and AC = 6 cm
    ∠ BAC = 90°
    As, BC is the diameter of the circle.
    ∴ BC = √AB² + AC²
    BC = √8² + 6²
    BC = √64 + 36

    Correct Option: E

    According to question , we draw a figure of a circle with two chords AB and AC ,

    Here , AB = 8 cm and AC = 6 cm
    ∠ BAC = 90°
    As, BC is the diameter of the circle.
    ∴ BC = √AB² + AC²
    BC = √8² + 6²
    BC = √64 + 36
    BC = √100 = 10 cm
    ∴ Radius of the circle = 5 cm


  1. The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends in the major segment of the circle is equal to









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    As per the given in question , we draw a figure circle

    AO = OB = AB
    ⇒ ∠AOB = 60°

    Correct Option: A

    As per the given in question , we draw a figure circle

    AO = OB = AB
    ⇒ ∠AOB = 60°
    [∵ ∆ AOB is equilateral]
    ∴ ∠ ACB = 30°



  1. The length of the chord of a circle is 8 cm and perpendicular distance between centre and the chord is 3 cm. Then the radius of the circle is equal to :









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    On the basis of question we draw a figure of circle with O centre ,

    AC = CB = 4 cm
    OC = 3 cm
    ∴ OA = √OC² + CA²
    OA = √3² + 4²

    Correct Option: B

    On the basis of question we draw a figure of circle with O centre ,

    AC = CB = 4 cm
    OC = 3 cm
    ∴ OA = √OC² + CA²
    OA = √3² + 4²
    OA = √9 + 16
    OA = √25 = 5 cm