[size=100]If you are not familiar with the construction steps necessary for the construction of the circumcircle of a triangle, you might want to explore the applet below. Just use the buttons of the [i]Navigation[/i][i] Bar[/i] in order to replay the construction steps. [/size]

[size=100]Construct a the circumcircle of a triangle that passes the Drag Test by following the construction steps provided below.[/size]

[table] [tr] [td][size=100]1.[/size][/td] [td][size=100][icon]/images/ggb/toolbar/mode_polygon.png[/icon][/size][/td] [td][size=100]Create an arbitrary triangle [i]ABC[/i].[/size][/td][/tr] [tr] [td][size=100]2.[/size][/td] [td][size=100][icon]/images/ggb/toolbar/mode_linebisector.png[/icon][/size][/td] [td][size=100]Construct the [i]Perpendicular Bisector[/i] for each side of the triangle.[br][u]Hint:[/u] The tool [i]Perpendicular Bisector[/i] can be applied to an existing segment.[/size][/td][/tr] [tr] [td][size=100]3.[/size][/td] [td][size=100][icon]/images/ggb/toolbar/mode_intersect.png[/icon][/size][/td] [td][size=100]Create intersection point [i]D[/i] of two of the line bisectors.[br][u]Hint:[/u] The tool [i]Intersect[/i] can be applied to the intersection of three lines or by successively selecting two of the three line bisectors.[/size][/td][/tr] [tr] [td][size=100]4.[/size][/td] [td][size=100][icon]/images/ggb/toolbar/mode_circle2.png[/icon][/size][/td] [td][size=100]Construct a circle with center [i]D[/i] through one of the vertices of triangle [i]ABC[/i].[/size][/td][/tr] [tr] [td][size=100]5.[/size][/td] [td][size=100][icon]/images/ggb/toolbar/mode_move.png[/icon][/size][/td] [td][size=100]Perform the Drag Test to check if your construction is correct.[/size][/td][/tr][/table][size=100][u][br]Hint[/u]: You might want to [url=https://tube.geogebra.org/student/mJoZDI7Zo]save your construction[/url] using the [img]https://wiki.geogebra.org/uploads/thumb/0/09/Menu-file.svg/16px-Menu-file.svg.png[/img] [i]File [/i]menu.[/size]

[size=100]Modify your construction to answer the following questions:[br][/size][list=1][*][size=100] Can the circumcenter of a triangle lie outside the triangle? If yes, for which types of triangles is this true?[br][/size][/*][*][size=100]Try to find an explanation for using line bisectors in order to create the circumcenter of a triangle.[/size][/*][/list]