Online Geometry: Similarity, Ratios, Proportions. Theorems and Problems. Page 4 of 5

Archimedes' Book of Lemmas.
Proposition 7, Similarity of Areas.

Archimedes' Book of Lemmas.
Proposition 10, Circle, Tangents, Chord, Parallel

Archimedes' Book of Lemmas.
Proposition 11, Perpendicular chords

I have used Geometry Expressions, the world's first Interactive Symbolic Geometry System, to visualize the Archimedean Twins and check out a variety of conjectures.

Geometry Problem 624
Triangle, Incenter, Excenter, Incircle, Excircle, Similarity.

Proposed Problem 131. Van Aubel Theorem, Concurrent Cevians, Sum of Ratios.

Proposed Problem 130. Triangle, Concurrent Cevians, Sum of Ratios.

Proposed Problem 129. Triangle, Concurrent Cevians, Sum of Ratios.

Proposed Problem 128. Incenter of a Triangle, Angle Bisectors, Sum of Ratios.

Proposed Problem 127. Centroid and Incenter of a Triangle, Parallel, Proportions.

Proposed Problem 126. Incenter of Triangle, Angle Bisector, Proportions.

Marion Walter's Theorem: Triangle and Hexagon areas: Using TracenPoche Dynamic Geometry Software

PProposed Problem 125. Area of Triangle, Star, Trisection of Sides.

PProposed Problem 124. Area of triangle, Similarity, Trisection of Sides.

Proposed Problem 123. Area of triangle, Similarity, Trisection of Sides.

Proposed Problem 122. Marion Walter's Theorem. Area of triangle and Hexagon, Trisection of Sides.

Proposed Problem 121. Similarity and Area of triangle, Trisection of Sides.

Proposed Problem 103.Equilateral Triangle Area, Interior Point, Heron's Formula.

Proposed Problem 79: Triangle. Similarity, Altitudes, Orthocenter, Incircles, Inradii.