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The bisectors of the angles B and C of ...

The bisectors of the angles B and C of a triangle `A B C` , meet the opposite sides in D and E respectively. If DE||BC , prove that the triangle is isosceles.

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The bisectors of the angles ABC and BCA of a triangle ABC meet in a point 0. What is the angle at O facing the side BC ?

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Knowledge Check

  • A triangle ABC is inscribed in a circle and the bisectors of the angles A, B and C meet the cir cumference at P, Q and R respec tively. The angles of the triangle PQR respectively are

    A
    `90^@ - A/2, 90^@ + A/2 90^@ + C/2`
    B
    `90^@ + A/2 , 90^@ - B/2 , 90^@ - C`
    C
    `90^@ - A/2 , 90^@ - B/2 , 90^@ - C/2`
    D
    None of these

  • The internal bisectors of angle B and angle C of triangle ABC meet at O. If angle A=80^@ then angle BOC is :

    A
    `50^@`
    B
    `160^@`
    C
    `100^@`
    D
    `130^@`

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    If the bisector of the vertical angle of a triangle bisects the base, prove that the triangle is isosceles.

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