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Math Help - Geometry question about a circle inscribed inside a triangle

  1. #1
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    Unhappy Geometry question about a circle inscribed inside a triangle

    Hello friends, I need help with a geometry question...
    http://s8.postimage.org/z1zbxoe39/Semicircle_Triangle.jpg this is the triangle.
    Here is what we know:
    1) PQ is the diameter of the semicircle.
    2) OE equals Radius
    3) PQ is parallel to BC
    4) AD is the altitude to BC
    5) BC = 20, AD = 15
    Now, the first part of the question asks us to prove that ABC and APQ have similarity. This I managed to do, so treat it as data.
    The second part is to find the radius, and this is where I'm stuck...
    Plz help me!
    I
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    Senior Member vincisonfire's Avatar
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    Re: Geometry question about a circle inscribed inside a triangle

    Begin with {PQ\over BC} = {AG\over AD}
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    Re: Geometry question about a circle inscribed inside a triangle

    Yes, I did that... And, according to the data, PQ is equal to 2R so: \frac{2R}{20}= \frac{AG}{15}
    But AG is unknown, and I don't have the ratio, so I don't understand what I'm supposed to do here. I'm supposed to find something about the small triangle, a relation or something, but I just can't find it... I'm guessing there is a theorem about a semi circle inscribed inside a triangle or something, but I don't know it...
    Last edited by chen888; January 11th 2013 at 11:35 AM.
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    Re: Geometry question about a circle inscribed inside a triangle

    Quote Originally Posted by chen888 View Post
    Yes, I did that... And, according to the data, PQ is equal to 2R so: \frac{2R}{20}= \frac{AG}{15}
    But AG is unknown, and I don't have the ratio, so I don't understand what I'm supposed to do here. I'm supposed to find something about the small triangle, a relation or something, but I just can't find it... I'm guessing there is a theorem about a semi circle inscribed inside a triangle or something, but I don't know it...

    Note that  AG=15-R . WHY?
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    Re: Geometry question about a circle inscribed inside a triangle

    Now I got it! Thanks! But I don't understand, I thought it was illegal to use the same data twice when doing 2 equations/variables... ugh I sat like an hour on this thing now it's solved so simply I feel like I got kicked in the nuts...
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    Senior Member vincisonfire's Avatar
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    Re: Geometry question about a circle inscribed inside a triangle

    Quote Originally Posted by chen888 View Post
    I thought it was illegal to use the same data twice when doing 2 equations/variables...
    There is only one equation {PQ\over BC} = {AG\over AD} and one unknown R. You can replace the length of the segments by any value depending on R.
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  7. #7
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    Re: Geometry question about a circle inscribed inside a triangle

    Ok I understand. Thanks very much for the help friends
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