Geometry

Overview

Geometry problems become clearer when the representation matches the structure. Use coordinates for computation, vectors for linear relations, inversion or transformations for circles, and synthetic facts when the diagram has strong incidence.

Checklist

• Draw a clean diagram and label all given data.
• Decide whether coordinates, vectors, complex numbers, or synthetic geometry is simplest.
• Hunt for cyclic quadrilaterals, equal angles, parallel lines, and homothety.
• Use area or power of a point when lengths multiply.
• Check degenerate or symmetric cases.

Common moves

• Put a key point at the origin or a line on an axis.
• Convert angle claims into dot products or slopes.
• Use similar triangles to replace hard lengths with ratios.
• Apply inversion when many circles or reciprocal distances appear.

Practice problems

Tags: geometry

Problem	Source	Difficulty	Tags
Starter Geometry Problem	Boilerplate	2	geometry, algebra