# Circumcircle of a Triangle Construction

##### Explore the construction of the circumcircle of a triangle
[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]
##### Task
[size=100]Construct the circumcircle of a triangle that passes the [i]Drag Test[/i] by following the construction steps provided below.[/size]
##### Construction steps
[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][table][tr][td][size=100][/size][/td][/tr][/table][table][tr][td]﻿6.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/td][td]Activate the [i]Move[/i] tool and select point [i]D[/i]. ﻿[/td][/tr][tr][td]﻿7.[/td][td][icon]https://wiki.geogebra.org/uploads/thumb/8/84/Menu-edit-rename.svg/32px-Menu-edit-rename.svg.png[/icon][/td][td]﻿Start typing the new name [i][code]Circumcenter[/code][/i] on the keyboard in order to open the [i]Rename[/i] dialog.[br][/td][/tr][tr][td]8.[/td][td][br][/td][td]﻿Select [button_small]OK[/button_small] to apply your changes and rename the point.[br][br][/td][/tr][/table]
##### Use your construction to answer the following questions
Can the circumcenter of a triangle lie outside the triangle? If yes, for which types of triangles is this true?
Try to think of a real world application in which finding the circumcenter of a triangle would be useful.[br]