Multiple Choice Question (MCQ)

In the figure, △ABC is a right triangle, where the internal angle \angle C = 90\degree , \angle A=30° , the segment AD bisects ∠A , which one is the value of the expression \dfrac{AB}{CD}-\dfrac{AC}{CD}

  1. ×

    \sqrt{3}

  2. \dfrac{\sqrt{3} }{3}

  3. ×

    3- \sqrt{3}

  4. ×

    6- 2\sqrt{3}

Collected in the board: Triangle

Steven Zheng posted 2 months ago


Answer

  1. Construct a perpendicular line from point D to AB and intersects AB at point D

    DE\perp AB .


    \dfrac{AB}{CD}-\dfrac{AC}{CD}

    =\dfrac{AB-AC}{CD}

    =\dfrac{BE}{CD}

    =\dfrac{BE}{DE}


    \because ∠DBE = 60\degree


    DB = 2BE

    DB^2=BE^2+DE^2


    4BE^2 = BE^2+DE^2

    3BE^2 = DE^2


    \therefore \dfrac{BE}{DE} = \dfrac{\sqrt{3} }{3}

Steven Zheng posted 2 months ago

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