Intersecting Chords Theorem (Proof)

Download the GeoGebra file: http://www.geogebratube.org/material/download/format/file/id/45955

Proof:
Join points A to C and points B to D.
\[\angle CAT = \angle BDT \;{\rm{ (common)}}\]
\[\angle CTA = \angle BTD \;{\rm{ (vert}}{\rm{. \;opp}}{\rm{. }}\;\angle {\rm{s)}}\]
\[\Delta ATC \;{\rm{ is \;similar \;to }}\;\Delta DTB.\;{\rm{ (AAA)}}\]
Therefore,
$$\begin{align}
\frac{{AT}}{{DT}} & = \frac{{CT}}{{BT}} \\
\\
AT \times BT & = CT \times DT \\
\end{align}$$