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Thread: Proof for a triangle problem.

  1. #1
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    Post Proof for a triangle problem.

    Hello!

    I'm having difficulty proving the following question. I know it's true, but I don't know what exactly to use.

    Let D on BC of triangle ABC so that D bisects angle BAC. Prove that AB >AC if and only if DB>DC.
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  2. #2
    Senior Member
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    Re: Proof for a triangle problem.

    Consider using the Law of Cosines ( https://en.wikipedia.org/wiki/Law_of_cosines ) and apply it to triangle ABD and triangle ACD to express BD^2 and CD^2. From here, you should be able to prove both directions of the if and only if statement.
    Let me know if you have further questions.

    Greetings from Calgary.
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