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I'm having some trouble figuring out this apparently easy question:

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Two circles touch internally at $T$. $TP$ is a chord of the smaller circle and the tangent at $P$ cuts the larger circle at $A$ and $B$ respectively. Prove that $PT$ bisects $\angle{ATB}$.

My current idea is to prove that $\triangle{APT}$ and $\triangle{BPT}$ are similar, however I cannot figure out how to do so.

user117363
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1 Answers1

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Hint: You have to argue with angles and not with similarity. What can you say about $\Delta QTP$ and what about $QT$ and $QP$?

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I'll can add more information if necessary.

ulead86
  • 3,381