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Math Help - Unable to get a step in the problem :(

  1. #1
    Senior Member
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    Exclamation Unable to get a step in the problem :(

    Hey guys



    The sides of triangle ABC are divided into segments of lengths a, b and x by the inscribed circle of centre O and radius r as shown. Find x in terms of a, b and r.

    The first part of the answer by the teacher is as shown:

    Let \angle OAB = \alpha and \angle OBA = \beta
    Therefore, \angle OCA = 90  (\alpha + \beta)

    So tan (90  (\alpha + \beta)) = \frac{x}{r}
    .

    Could someone please explain to me how tan (90  (\alpha + \beta)) = \frac{x}{r}? For some reason, all I seem to be able to get is tan (90  (\alpha + \beta)) = \frac{x}{r}.

    Thanx.
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  2. #2
    MHF Contributor red_dog's Avatar
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    O is the intersection of the bisectors of the angles of triangle.

    Then \widehat{A}=2\widehat{OAB}=2\alpha, \ \widehat{B}=2\widehat{OBA}=2\beta

    \widehat{OCA}=\frac{1}{2}\widehat{C}=\frac{1}{2}(1  80-2(\alpha+\beta))=90-(\alpha+\beta)
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