Geometric context:[list=1][*]Consider a line [b]f[/b] and a point [b]C[/b] defined on that line. Let's draw a circle [b]c[/b] with centre [b]C[/b] and radius [b]CR[/b].[br][/*][*]Consider a point [b]B[/b] on [b]f[/b], and point [b]A[/b] on the circle. Reflect point [b]A[/b] with respect to line [b]f[/b] to determine point [b]A'[/b].[/*][*]Finally, we draw the lines [b]AB[/b] and [b]A'C[/b]; these lines intersect at [b]D[/b]. What is the locus of point [b]D[/b] when point [b]A[/b] is moved across the circle?[/*][/list][br]Explore the following in the applet: [br][list][*]Move the point [b]A[/b] and pay attention to point [b]D[/b]. Click [b]Animate A[/b] for automatic motion.[br][/*][*]Activate the trace of [b]D[/b] to help you to observe a pattern. [br][/*][*]Change the position of [b]B[/b] along the line [b]f, [/b]and move [b]A[/b] again.[br][/*][/list]

In the following applet, select the tool [b]Locus[/b] [icon]/images/ggb/toolbar/mode_locus.png[/icon] and apply it to the point [b]D[/b] when [b]A[/b] is moved.[br]Then, move only the point [b]B [/b]and observe what happens to the locus of [b]D[/b]. Click on [b]Animate B[/b] for automatic motion.[br][br]Questions:[br][list][*]What happens if [b]B[/b] is within the segment [b]EE'[/b]? [/*][*]What happens if [b]B[/b] is not in the segment [b]EE'[/b]? [/*][*]What happens if [b]B[/b] is equal to [b]E [/b]or[b] E'[/b]?[/*][/list][color=#ff0000]Note:[/color] The segment [b]EE'[/b] is equal to 4[b]CR[/b].