Circumcenter - 2019

Follow the steps below to construct the circumcenter.
Use [icon]/images/ggb/toolbar/mode_linebisector.png[/icon] to construct the perpendicular bisector of segments AB, BC and AC.[br]Use [icon]/images/ggb/toolbar/mode_intersect.png[/icon] to add a point where the three perpendicular bisectors intersect. [br]Use [icon]/images/ggb/toolbar/mode_showhidelabel.png[/icon] to label the point where the perpendicular bisectors intersect.
[b][color=#cc0000]The point where all three perpendicular bisectors intersect is called the circumcenter. [/color][/b][br][br]1. Use [icon]/images/ggb/toolbar/mode_move.png[/icon] to move point A, B or C so that the [b][color=#cc0000]circumcenter[/color][/b] is outside the triangle. What do you notice about the triangle?
2. Use [icon]/images/ggb/toolbar/mode_move.png[/icon] to move point C so that the [b][color=#cc0000]circumcenter[/color][/b] lies on a side of the triangle. What do you notice about the triangle?
We are now going to learn about the properties of a circumcenter.
[br]Use [icon]/images/ggb/toolbar/mode_segment.png[/icon] to draw a segment from A to the [b][color=#cc0000]circumcenter[/color][/b].[br]Use [icon]/images/ggb/toolbar/mode_distance.png[/icon] to measure the length of the segment from A to the [b][color=#cc0000]circumcenter[/color][/b].[br]Repeat the process for vertex B and C[br]Use [icon]/images/ggb/toolbar/mode_circle2.png[/icon] to draw a circle with center at the [color=#cc0000][b]circumcenter[/b][/color] and through point A.
Circumcenter Properties
3. Use [icon]/images/ggb/toolbar/mode_move.png[/icon]to move point A, B or C around. What do you notice about the dashed segment lengths?
The Circle
4. You constructed the circle to go through point A. When you move the triangle, you should notice that the circle also always goes through B and C. Why is that?
Application for Circumcenter
5. For which of the following situations, would it make sense to find the [b][color=#cc0000]circumcenter[/color][/b]?
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Information: Circumcenter - 2019