We have two types of tangent circles.
Here are GSP files for these two tangent circle types.
An image for tangent circles.
An image for style 1 type tangent circles. Here we animated the point E around the circle and traced the blue circle. When we animate the point E then the blue circle trace around the circle which is inside of the big circle.
Here we used the same method for style 2 type of tangent circles. Here point E animated around the circle and the red circle traced. The red circle trace around the green circle.
An image for style1 type of tangent circles. Here we animated the point E and traced the perpendicular line. As you can see after we traced the perpendicular line then we got an elliptical shape inside the green circle.
Here we animated the point E again but we traced the perpendicular line for style 2. As you can see not traced area looks like an ellipse.
