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Math Help - triangle problem

  1. #1
    Member helloying's Avatar
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    triangle problem

    see the picture attaced and many thanks to people who will help me solve this problem and the other problems I have posted before. I really appreaciate the contributors very much.I give thanks to everyone that answer to my question
    Attached Thumbnails Attached Thumbnails triangle problem-img003.jpg  
    Last edited by helloying; August 15th 2008 at 08:00 PM. Reason: i forgot to attach the picture.
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  2. #2
    o_O
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    You can find \angle OAB by extending O to AB, thereby bisecting it. Now, recall that a circle's tangent forms a right angle with its radius at their point of intersection - i.e. \angle OAT = 90^{\circ}. You can then find \angle BAT = \angle OAT - \angle OAB.

    Now extend a horizontal line from the middle of AB (call this point S) to point T (again bisecting AB to form AS and SB). Now we have a right triangle, \triangle SAT. You can then use trigonometry to find TA since: \cos \left(\angle  BAT\right) = \frac{AS}{TA} \: \: \iff \: \: TA = \frac{AS}{\cos \left(\angle BAT \right)}
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