Locus of an Ellipse Guided by Two Tangent Circles

This example demonstrates how, under the constraint of two tangent circles, a moving construction leads to a locus that matches an ellipse-like trace. It combines circle tangency and symmetry with classical locus reasoning: as certain points are defined via tangents, angle bisectors, and orthogonal relations, their motion traces an elliptical curve. Key concepts include geometric characterization of an ellipse, circle tangency (tangent line conditions), symmetry (e.g., bisectors and equal-distance relationships), and the locus method for deriving curves from constraints. Construction highlights in GeoGebra: Ray and Circle to define rays and circles; Intersect to find key intersection points; Rotate and LineBisector to set symmetric/rotated configurations; Tangent and OrthogonalLine to enforce tangency and perpendicular relations; Line, Segment, Midpoint, Distance, Arc, and Vector for geometric measures and supporting constructions; Ellipse as a reference object and Locus plus Sequence to generate the traced curve from the evolving point set. Suitable for secondary school geometry, contest preparation, and anyone learning geometric construction and curve tracing.