[b][i]Theorem[/i][/b]: If two lines intersect at point [math]M[/math] and intersect a circle at points [math]P, Q, R[/math] and [math]S [/math] respectively, then [math]MP \cdot MQ[/math] = [math]MR \cdot MS[/math][br][br]Drag the blue points to the following configurations and see the products [math]MP \cdot MQ[/math] and [math]MR \cdot MS[/math]. In each case, see why the corresponding angles in the blue and brown triangles are congruent.[br][br][list][*]M - outside the circle;[/*][*]M - inside the circle;[/*][*]M - on the circle;[/*][*]P=Q and R different than S;[/*][*]P=Q and R=S[/*][/list]