We can set a point such that it can be confined on a "path" e.g. a line, an arc, sides of a polygon etc or in a "region" e.g. a sector, a polygon etc. To create such a point, we can use the command [b]Point(path)[/b] and [b]PointIn(Region)[/b] respectively.[br][br]The following is an example about angles in alternate segment. The point Q is restricted on the arc PQR.[br][br][b][u]Classwork[/u][/b]: Create a point on the tangent line and a point in the gray region in the GeoGebra applet below. Then use the Attach / detach tool [icon]/images/ggb/toolbar/mode_attachdetachpoint.png[/icon] to detach the points.[br][br]

You can also construct irregular regions using inequalities and boolean operations.[br][br][b][u]Classwork[/u][/b]: Create a point that is in the region bounded by the parabola [math]y=2-x^2[/math] and [math]y=|x| [/math] in the GeoGebra applet below.[br][br](Hint: You can use "&&" to obtain the intersection of two regions defined by the inequalities.)[br][br]