Homothety helps solve problems

Homothety is a transformation that enlarges or shrinks figures from a fixed point (the center) by a certain ratio. In problem solving, homothety can simplify geometric configurations by transforming complicated figures into similar, often easier-to-analyze figures.

Important properties

• Homothety preserves the shape of figures but changes their size.

• Lines passing through the center of homothety remain unchanged (they are invariant).

• Corresponding points, lines, and circles in the original and image figures are collinear with the center.

• Homothety maps circles to circles and lines to lines.

• Homothety can be used to relate tangent circles, parallel lines, and similar triangles.