Construct the incircle of a triangle by following the construction steps below.
[table][tr id=triangle_1][td]1.[/td][td][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_polygon.png[/icon][/td][td]Select tool [i]Polygon[/i]. Create an arbitrary triangle [i]ABC[/i] by clicking three times in the [i]Graphics View[/i]. Close the triangle by selecting the first point [i]A[/i] again.[/td][/tr][tr id=step2][td]2.[/td][td][icon]/images/ggb/toolbar/mode_angularbisector.png[/icon][/td][td]Activate tool [i]Angle Bisector.[/i] Construct the [i]Angle Bisector[/i] for two angles of the triangle by successively selecting the three corners.[br][u]Hint[/u]: You can find this tool in the [i]Special Lines Toolbox [/i](fourth [i]Toolbox[/i] from the left).[/td][/tr][tr id=intersection_3][td]3.[/td][td][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/td][td]Create [i]intersection point[/i] [i]D[/i] of the two angle bisectors.[br][u]Hint:[/u] Successively select the two angle bisectors, or click directly on the intersection point. [/td][/tr][tr id=perpendicular_4][td]4.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_orthogonal.png[/icon][/td][td]Select tool [i]Perpendicular line[/i]. Create a perpendicular line between one side of the triangle and the point [i]D[/i].[/td][/tr][br][tr id=intersection_5][td]5.[/td][td][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/td][td]Create [i]intersection point[/i] [i]E[/i] of the perpendicular line [i]h[/i] and the chosen side of the triangle.[/td][/tr][/table]
[table][tr id=circle_6][td]6.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_circle2.png[/icon][/td][td]Construct the incircle with center [i]D[/i] through point [i]E[/i].[br][u]Hint[/u]: First, select point [i]D[/i], then point [i]E[/i].[br][/td][/tr][tr id=HideLines][td]7.[/td][td][icon]/images/ggb/toolbar/mode_showhideobject.png[/icon][br][/td][td]Hide the three auxiliary lines used for the construction.[/td][/tr][tr id=Tool8][td]8.[/td][td][icon]/images/ggb/toolbar/mode_segment.png[/icon][br][/td][td]Connect points D and E using a segment in order to display the radius of the incircle.[/td][/tr][tr id=Tool7][td]9.[/td][td][icon]/images/ggb/toolbar/mode_angle.png[/icon][br][/td][td]Show the right angle between the incircle's radius and the corresponding side of the triangle.[/td][/tr][tr id=moveTriangle][td]10.[/td][td][icon]https://tube.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/td][td]Select the [i]Move[/i] tool and drag the vertices of the triangle in order to check if your construction is correct.[/td][/tr][/table]