[color=#000000]Use any of the tools in the limited toolbar below to construct this triangle's circumcircle. [br][br]You can use the slider to change the measure of angle [i]A[/i] at any time. [br]Feel free to move the triangle's white vertices around as well. [br][br]Feel free to reference [url=https://www.geogebra.org/m/ueV9RpZf]this worksheet[/url] at any time. [/color]
[color=#980000][b]Recall that the circumcenter is the center of a triangle's circumcircle. [br][/b][/color][br][b][color=#000000]Questions: [/color][/b][br][br][color=#000000]1) Is it ever possible for a triangle's circumcenter to lie OUTSIDE the triangle? I[br] If so, under what circumstance(s) will this occur?[br][br]2) Is it ever possible for a triangle's circumcenter to lie ON THE TRIANGLE ITSELF? [br] If so, under what circumstance(s) will this occur? [br] [br]3) If your answer for (2) was "YES", where on the triangle did the circumcenter lie?[br] Use the tools of GeoGebra to validate your response. [br][br][/color][color=#000000]4) Is it ever possible for a triangle's circumcenter to lie INSIDE the triangle? [br] If so, under what circumstance(s) will this occur?[/color]