Geometric Problems by Homothety

Below is a list of problems either defined in terms of homothety or for which there is a solution exploiting the homothety transformation.

1. Homothety
2. Three circles and common tangents
3. Napoleon's Theorem, A Generalization
4. Tucker Circles Through Homothety
5. Monge via Desargues
6. Remarkable Line in Cyclic Quadrilateral
7. A Characterization of the Euler Line
8. Mixtilinear Circles and Concurrence
9. Two Circles Inscribed in a Parallelogram
10. Point common to two similar rectangles
11. Nagel Line
12. Concyclic Circumcenters: A Sequel
13. Four Touching Circles
14. Circle Inscribed in a Circular Segment
15. Perpendicular Bisectors in an Inscriptible Quadrilateral II
16. Concyclic Circumcenters: A Dynamic View
17. Four Centroids and Parallels
18. Parallel Lines in a Quadrilateral
19. Concurrency in the Intouch Triangle
20. Similar Triangles on Sides of a Quadrilateral
21. Homologous Lines under Three Spiral Similarities
22. The Menelaus Theorem
23. Nagel Point of the Medial Triangle
24. Homothety between In- and Excircles
25. Many more examples could be obtained by searching this site.

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