Given five circles centered on a common sixth circle and intersecting each other chainwise on the same circle, the lines joining their second intersection points forms a pentagram whose points lie on the circles themselves

Orthoptics

Simson Line

Circle Power

Radical Axis

Radical Axis - Pencil of Circles

Radical Center

Circle Inversion

Circle Inversion - Circles and Lines

Circle Polar Line

Circle Polar Line Reciprocity

Exterior Point

Interior Point

Exterior Point - Bitangent Circle

Interior Point - Bitangent Circle

D'Alembert Theorem

Apollonius Tangency Problem

Apollonius Tangency Problem

Apollonius Tangency Problem - 8 circles

Miquel's Theorem

Clifford's Theorem

Five Circles Theorem

Given five circles centered on a common sixth circle and intersecting each other chainwise on the same circle, the lines joining their second intersection points forms a pentagram whose points lie on the circles themselves