Plane Geometry


  1. A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time a tower casts the shadow 40 m long on the ground. Find the height of the tower.











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    Draw a figure as per given question,
    In ΔACB and PCQ
    ∠C = ∠C (common)
    ∠ABC = ∠PQC (each 90°)
    ∴ ΔACB ∼ ΔPC (AA Similarity)


    Correct Option: C

    In ΔACB and PCQ
    ∠C = ∠C (common)
    ∠ABC = ∠PQC (each 90°)
    ∴ ΔACB ∼ ΔPC (AA Similarity)

    AB=BC
    PQQC

    h=4000
    128

    h = 60m



  1. If angles of measure (5y + 62°) and (22° + y) are supplementary, then value of y is :









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    As we know that Sum of two supplementary angles = 180°
    ∴ ( 5y + 62° ) + ( 22° + y ) = 180°
    ⇒ 6y + 84° = 180°
    ⇒ 6y = 180° – 84° = 96°

    Correct Option: A

    As we know that Sum of two supplementary angles = 180°
    ∴ ( 5y + 62° ) + ( 22° + y ) = 180°
    ⇒ 6y + 84° = 180°
    ⇒ 6y = 180° – 84° = 96°

    ∴ y =
    96
    = 16°
    6



  1. ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120° and ∠BAC = 30°, then ∠BCD is :









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    As per the given in question , we draw a figure of a quadrilateral ABCD inscribed in a circle with centre O

    Given , ∠COD = 120°
    ∠BAC = 30°

    ∠CAD =
    1
    × ∠COD
    2

    ∠CAD =
    1
    × 120° = 60°
    2

    Correct Option: B

    As per the given in question , we draw a figure of a quadrilateral ABCD inscribed in a circle with centre O

    Given , ∠COD = 120°
    ∠BAC = 30°

    ∠CAD =
    1
    × ∠COD
    2

    ∠CAD =
    1
    × 120° = 60°
    2

    ∴ ∠BAD = 90°
    ∴ ∠BCD = 180° - ∠BAD
    ∴ ∠BCD = 180° – 90° = 90°


  1. The radius of two concentric circles are 9 cm and 15 cm. If the chord of the greater circle be a tangent to the smaller circle, then the length of that chord is









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    According to question , we draw a figure of a circle with centre O ,

    Here , BO = OC = 15 cm and OD = 9 cm.
    From ∆ BDO ,
    ∴ BD = √BO² - OD²

    Correct Option: A

    According to question , we draw a figure of a circle with centre O ,

    Here , BO = OC = 15 cm and OD = 9 cm.
    From ∆ BDO ,
    ∴ BD = √BO² - OD²
    ∴ BD = √15² - 9²
    BD = √24 × 6 = 12 cm
    ∴ BC = 2 × 12 = 24 cm.



  1. The distance between the centres of the two circles of radii r1 and r2 is d. They will touch each other internally if









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    According to question , we can draw a figure

    Correct Option: C

    According to question , we can draw a figure

    Hence , option C is correct answer .