Problem 4_1
GeoGebra Construction:
Problem 4_1
Given three noncollinear points A, B, C, construct three mutually tangent circles with centers A, B, C.
Solution:
I created 3 points, A, B, and C (noncollinear). Then, I made segment AB and the midpoint of AB. I then, constructed a circle with center A and through the midpoint of AB and a circle with center B and through the midpoint AB. These two circles are tangent at the midpoint of AB. I then created segments AC and BC. I created the midpoints and a circle with the same radius as circle A and circle B. Circle C is tangent to A at the midpoint of AC and tangent to circle B at the midpoint of BC.
EDITED:
I created a regular polygon with 3 sides. I then created the three angle bisectors and their intersection points. I then created 3 circles with centers A, B, and C and radius from the center to the intersection point of the angle bisector.