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Thread: Tangets of a circle

  1. #1
    Senior Member
    Nov 2007

    Tangets of a circle

    The lengths of the tangents drawn from the points $\displaystyle A$ and $\displaystyle B$ to a circle $\displaystyle k$ are $\displaystyle a$ and $\displaystyle b$, respectively. We know that $\displaystyle \frac{AT}{a}=\frac{BT}{b}$ (and $\displaystyle A, B, T$ are not collinear.) Prove that the circle passing through the points $\displaystyle A, B, T$ touches $\displaystyle k$.
    Attached Thumbnails Attached Thumbnails Tangets of a circle-circle_with_tangents_cropped.png  
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