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ABC is a triangle with ∠BAC=60∘,AB=5 and AC=25. D is a point on the internal angle bisector of ∠BAC such that BD=DC. What is AD^2?

  • maths -

    using the law of cosines, if we let AD=x,

    x^2 + 5^2 - 2x(5)cos30 = x^2 + 25^2 - 2x(25)cos30

    25-5x√3 = 625-25x√3
    20x√3 = 600
    x = 30/√3
    x^2 = 300

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