Geometric Construction 1

An ellipse is the locus of a point which moves so that the sum of its distances from two fixed points (the loci) is a constant.

Fix a point P inside a circle C. Show that the line perpendicular to the line segment joining P and a variable point Q on C envelopes an ellipse.

Given a point outside an ellipse,
construct the pair of tangents to the ellipse passing through the point.

Given a point and a circle, find the locus of the circle passing through the point and tangent to the circle. There are four cases to consider:

Given two circles, find the locus of the center of the common tangent circle.
There are several cases to consider: