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Bisectors of angles A, B and C of a tri...

Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E andF respectively. Prove that the angles of the triangle DEF are `90o-1/2A`,`90o-1/2B`and `90o-1/2C`

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Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are 90o-1/2A ,90o-1/2B and 90o-1/2C

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

Knowledge Check

  • If the angles of a triangle ABC are in the ratio 2:3:1 then the angles A,B and C are

    A
    `angle A=60^@,angelB=90@^@,angleC=30^@`
    B
    `angle A=40^@,angelB=120@^@,angleC=20^@`
    C
    `angle A=20^@,angelB=60@^@,angleC=60^@`
    D
    `angle A=45^@,angelB=90@^@,angleC=45^@`

  • If angle C of a triangle ABC be 90^(@) , then tan A + tan B =

    A
    `( a^(2))/( bc)`
    B
    `(b^(2))/( ca)`
    C
    `(c^(2))/(ab)`
    D
    `a+b`

  • Internal bisectors of angles /_B and /_C of a triangle ABC meet at O. If /_BAC = 80^@ , then the value of /_BOC is

    A
    `120^@`
    B
    `140^@`
    C
    `110^@`
    D
    `130^@`

    • Similar Questions

    Explore conceptually related problems

    Bisector of the angles B and C of an isosceles triangle ABC with Ab = AC intersect each other at O. Shown that external angle agjacent to angleABC is equal to angleBOC .

    The circumcentre of the triangle ABC is O . Prove that angle OBC+angle BAC=90^@ .

    In triangle ABC,the bisector of interior angle A and the bisector angle C meet at point O. Prove that angle AOC=(1)/(2)angleB

    In DeltaABC , bisectors of angleB and angleC interesct each other at point O. Prove that angleBOC=90^(@)+(1)/(2)angleA i.e., angle1 =90^(@)+(1)/(2)

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

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