Plane Geometry


  1. The sides AB and AC of ΔABC have been produced to D and E respectively. The bisectors of ∠CBD and ∠BCE meet at O. If ∠A = 40°, then ∠BOC is equal to:













  1. View Hint View Answer Discuss in Forum

    As we know the formula,

    ∠BOC = 90° -1∠A
    2

    Correct Option: D

    As we know the formula,

    ∠BOC = 90° -1∠A
    2

    ∴∠BOC = 90° -1(40°)
    2

    = 90° - 20°
    ∠BOC = 70°


  1. In the given figure, DE || BC if AD = 1.7 cm, AB = 6.8 cm and AC = 9 cm, find AE.













  1. View Hint View Answer Discuss in Forum

    Since DE || BC, We can use the formula,

    AB = AC
    ADAE

    Correct Option: A

    Since DE || BC,

    AB = AC
    ADAE

    68 = 9
    17AE

    or , AE = 9 = 2.25cm
    4



  1. If the bisector of an angle of Δ bisects the opposite side, then the Δ is :











  1. View Hint View Answer Discuss in Forum

    According to given question, ∠1 = ∠2

    AB = BD
    ACAD


    Correct Option: B

    Since ∠1 = ∠2

    AB = BD
    ACAD

    But BD = CD (given)
    AB = 1
    AC

    AB = AC
    ∴ the given ∆ is isosceles



  1. The areas of two similar Δs are 81 cm2 and 144 cm2. If the largest side of the smaller Δ is 27 cm, then the largest side of the larger Δ is :













  1. View Hint View Answer Discuss in Forum

    Let ABC and DEF be the two similar Δs having area 81 cm2 and 144 cm2 respectively:
    Let BC = 27 cm
    Then since ΔABC ∼ ΔDEF

    area (∆ABC) = BC2(area Theorem)
    area (∆DEF)EF2

    Correct Option: C

    Let ABC and DEF be the two similar Δs having area 81 cm2 and 144 cm2 respectively:
    Let BC = 27 cm
    Then since ΔABC ∼ ΔDEF

    ar (∆ABC) = BC2(area Theorem)
    ar(∆DEF)EF2

    81 = (27)29 = 27
    144x212x

    ∴ x = 36 cm.



  1. In the given figure ∠BAD = ∠CAD. AB = 4 cm, AC = 5.2 cm, BD = 3 cm. Find BC.













  1. View Hint View Answer Discuss in Forum

    According to question, Given that
    ∠BAD = ∠CAD. AB = 4 cm, AC = 5.2 cm, BD = 3 cm
    In ΔABC, AD is the bisector of ∠A

    AB=BD(Internal bisector prop.)
    ACCD

    Correct Option: A

    According to question, Given that
    ∠BAD = ∠CAD. AB = 4 cm, AC = 5.2 cm, BD = 3 cm
    In ΔABC, AD is the bisector of ∠A

    AB=BD(Internal bisector prop.)
    ACCD

    4=3⇒ DC = 3.9 cm
    5.2DC

    But BC = BD + CD = 3cm + 3.9 cm = 6.9 cm