GeoGebra Classroom

# Construction: Circumscribed and Inscribed Circles

## Construction-1: Inscribed Circle

Construct an inscribed circle to the given triangle. Take a screen shot of your final image and save it into your assignment for today, then submit to the dropbox for today. Be sure to show all steps. (You can zoom in on the triangle to see better, a tip if you mess up and want to delete something, select the pointer tool then hit delete on your keyboard) 1) Construct the angle bisector of one side of the triangle    ﻿a) Place a point D on the segment AB where D is closer to A than to B    ﻿b) Create a compass circle with a center A and radius of D by clicking the circle tool--> dropdown to compass.  Then click point D first, then A and a compass circle will appear    ﻿c) Now label where that compass circle crosses AC with point E.    ﻿d) Create a compass circle with center D and radius of AD    ﻿e) Create a compass circle with center E and radius AE.      ﻿f) Create a point F where those two compass circles intersect    ﻿e) Create a line AF using the line tool. This is the angle bisector of angle BAC 2) Construct the angle bisector of the other side of the triangle    ﻿a) Repeat the steps above for angle ABC 3) Create a point J of their intersection which is called the INCENTER 4)Mark the intersection of line BI with side AC with point K 5) Select the Circle tool, then the drop down "Circle through a center and a point".  Select J for the center and point K for the point.  Your Inscribed Circle will be created with Center J, through points D and G. 6) Use the ABC tool to type your name next to your construction before you screenshot it.

## Construction 2: Circumscribed Circle

Construct a Circumscribed circle to the given triangle. Take a screen shot of your final image and save it into your assignment for today, then submit to the dropbox for today. Be sure to show all steps. (You can zoom in on the triangle to see better, a tip if you mess up and want to delete something, select the pointer tool then hit delete on your keyboard)) 1) Construct a Perpendicular Bisector of One Side of the Triangle ﻿a) Choose Perpendicular Bisector from the 4th drop down menu, then select AB 2) Construct a Perpendicular Bisector of another side of the triangle ﻿a) Choose Perpendicular Bisector from the 4th drop down menu, then select BC 3) Create a point D, at their intersection, by choosing the intersect point from the 2nd drop down ﻿a) Choose Intersect then select the perpendicular bisectors you created. Point D will then be created. 4) This is the center of the circumscribed circle, which is called the circumcenter. 5) Select the Circle Button- then choose "Circle through center and point". Select D as the center, then choose any of the vertices of the triangle. A circle will be created that goes through all 3 points of the triangle and has a center at D. 6) Use the ABC tool to type your name next to your construction before you screenshot it.