Finding the center of a circle – intersecting circles
Using the Geogebra software one can move one of the circles (closer or farther apart), with the points C and E remaining fixed and the chords passing through the points of intersection of the circles. After moving the circle there are several options: 1. The chords CF and ED do not intersect and a trapezoid is formed. 2. The chords CF and ED intersect at a point on the circle (F and D coincide) and a trapezoid is not formed. 3. The chords CF and ED intersect inside the circle and a trapezoid is formed. 4. The circles are tangent to each other from the inside or from the outside (A and B coincide). The chords CF and ED intersect at the point of tangency and a trapezoid is formed.