each image below links to a step‑by‑step GeoGebra applet, where you can move forwards and backwards through the construction or watch a short animation of how it unfolds. in some applets, the blue circular points are movable. these applets are also collected in this GeoGebra book.
tangents to a circle, from an exterior point

tangents common to two equal circles

tangents common to two different circles

interior tangents common to two different circles

ellipse, given its axes #01

ellipse, given its axes #02

tangent and normal to the ellipse

foci of a given ellipse

tangents to an ellipse, from an exterior point

tangent to an ellipse, given its direction
