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Math Help - Another triangle circumscribed about a circle

  1. #1
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    Another triangle circumscribed about a circle

    A triangle ABC, where A= 60 degree. Let O be the inscribed circle of triangle ABC. Let D,E and F be the point.?

    at which circle O is tangent to the side AB, BC, and CA. And Get G be the point of intersection of the line segment AE and the circle O. Set x =AD.

    1. the triangle ADF/ ( AG*AE) = ?

    2. when BD=4 and CF=2, then BC=? and x satisfy the equation x^2 + Bx-C =0 find the value of B and C

    3. AD =?

    I heard from my friend that there is a property to easily get AE*AG for the first number. I just can't seem to find it or realize what it is. Or is there any other way to get this?
    I know so far that all the formed triangles; ADF, DBE, ECH are all isosceles triangles and that the center of the circle to a vertex of the triangle will bisect it's angle
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  2. #2
    Super Member
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    Hi gundanium,
    You are referring to tangent-secant theorem. Look it up.



    bjh
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  3. #3
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    Oh wow. I had no idea this even existed. Thank you very much!
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