Use the applet below to explore the Tangent-Secant Theorem and its proof. 
Corollary: Intersecting Chords & Intersecting Secants Theorem 
Move points P and A about to explore the 3 different theorems that are interconnected: (i) Intersecting Chords Theorem, (ii) Intersecting Secant Theorem, and (iii) Tangent-Secant Theorem.  
Try to prove them using similar triangles.