Summarize the properties and construction of perpendicular lines, points, and circles.[br][br][u]Hint[/u]: If you are not familiar with the construction steps necessary for the perpendicular line through a point NOT on the line construction, you might want to explore the applet below. Just use [br]the buttons of the [i]Navigation[/i][i] Bar[/i] in order to replay the construction steps.

[table][tr][td][size=100]1.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_point.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100]Construct another point on line AB. [br](point D)[/size][/size][/size][/size][/td][td][br][/td][td][size=100]5.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Create circle [i]DE[/i]. (Circle e)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][size=100][size=100][size=100][/size][/size][/size][/size][/td][/tr][tr][td][size=100][/size][/td][td][size=100]Hint:[/size][/td][td][size=100][size=100][size=100]Be sure to test that when you move point D it stays attached to line AB.[/size][/size][size=100][size=100][size=100][size=100][size=100][size=100][size=100][/size][/size][/size][/size][/size][/size][/size][br][/size][/td][td][br][/td][td][size=100]6.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Construct the intersection points between circles d & e. [br](points F & G)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/td][/tr][tr][td][size=100][size=100][size=100]2.[/size][/size][/size][/td][td][size=100][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Create circle [i]CD[/i]. (Circle c)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/td][td][br][/td][td][size=100]7.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_join.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Create line [i]FG[/i]. (line g)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/td][/tr][tr][td][size=100]3.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/td][td][size=100]Construct the second intersection point between circle c and line AB. [br](point E)[br][/size][/td][td][size=100][br][/size][/td][td][br][/td][td][size=100][size=100][size=100][size=100][icon]https://wiki.geogebra.org/uploads/thumb/0/0c/Mode_segment.svg/120px-Mode_segment.svg.png[/icon][/size][/size][/size][/size][/td][td][size=100][/size][size=100][size=100][size=100][size=100][size=100][size=100][/size][/size][/size][/size][/size][/size][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]You can construct segment EF and FD to explore their relationship.[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][br][/td][/tr][tr][td][size=100]4.[/size][/td][td][size=100][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td][td][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100][size=100]Create circle [i]ED[/i]. (Circle d)[/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/size][/td][td][br][/td][td][size=100][/size][/td][td][size=100][icon]https://wiki.geogebra.org/uploads/thumb/0/0c/Mode_segment.svg/120px-Mode_segment.svg.png[/icon][/size][/td][td][size=100]You can also construct segment EG and GD to explore their relationship.[/size][/td][/tr][/table]