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ABC is cyclic triangle. The bisectors of...

ABC is cyclic triangle. The bisectors of the angles of the triangle intersect the circumeference of the circle at X,Y and Z. Prove that the measuremnts of the angles of the `Delta XYZ` are `90^(@)-(A)/(2), 90^(@)-(C)/(2)` respectively.

Answer

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Knowledge Check

  • The angle between the bisectors of two acute angles of a right angled triangle is

    A
    `90^@`
    B
    `(112)1/2^@`
    C
    `135^@`
    D
    `120^@`

  • The perpendicular bisector of the three sides of a right - angled triangle intersect each other

    A
    at right angular point
    B
    outside the right- angled triangle
    C
    inside the right - angled triangle
    D
    at the mid-point of the hypotenuse of the right - angled triangle

  • If the bisector of angle A of triangle ABC makes an angle theta with BC, then sin theta is

    A
    `"cos"((B-C)/2)`
    B
    `sin"((B-C)/2)`
    C
    `sin"(B-A/2)`
    D
    `sin"(C-A/2)`

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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 90^@-1/2A , 90^@-1/2B and 90^@-1/2C

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    Delta ABC is inscirbed in a circle, the bisector of the angles angle BAC, angle ABC and angle ACB intersect at the point X,Y,Zon the circle repectively. Prove that in Delta XYZ , angle YXZ=90^(@)-(1)/(2) angle BAC

    If the bisector of an angle of a triangle also bisects the opposite side, prove that the triangle is isosceles.

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