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Math Help - Geometry - triangle problem

  1. #1
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    Geometry - triangle problem

    ABC is a triangle in which \angle B = 2 \angle C. If D is a point on BC such that AD bisects \angle BAC and AB =CDProve that \angle BAC = 72^{\circ}

    Can we go this way :

    Let \angle A = 2t ;  \angle B = 2x ; \angle C = x[/latex] ( as \angle B = 2\angle C Let \angle ADC = m ; \angle ADB =n such that \angle m + \angle n = 180^{\circ}

    Now in \triangle ADB ; 2x+n+t =180^{\circ}( since \angle A = 2t and D is the bisector of \angle BAC also \angle m + \angle x + \angle DAC = 180^{\circ}

    \angle m = \angle n + \angle 2x( as m is external angle which is equal to sum of the opposite interior angles)
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  2. #2
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    Re: Geometry - triangle problem

    Geometry - triangle problem-triangle-15-mar-13.png
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  3. #3
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    Re: Geometry - triangle problem

    thanks a lot...
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