🧩 Problem Types

Master the art of pattern recognition in AMC geometry. This catalog helps you identify common problem setups and apply the right solution strategies.

🎯 Pattern Recognition Strategy

Step 1: Identify the Setup

• Look for key geometric configurations
• Identify given information and what’s being asked
• Check for special properties or relationships

Step 2: Apply the Template

• Use the appropriate solution template
• Follow the standard approach for that problem type
• Adapt the template to the specific problem

Step 3: Verify and Check

• Ensure your solution makes geometric sense
• Check for common pitfalls
• Verify units and final answer

📚 Problem Type Catalog

🔺 Triangle Patterns

• Angle Chase Cycles - Inscribed angles, parallel lines, cyclic triggers
• Similar Triangle Stacks - Parallel lines, homothety, “gaps”/ladder problems
• Area Ratio in Triangle - Medians/cevian splits, barycentric-like ratios

⭕ Circle Patterns

• Tangent-Secant-Chord - Equal tangents, PoP, intersecting chords/secants
• Cyclic Quad Setups - Equal subtended angles, Ptolemy applications
• Circle Packing Touching - Chains of tangencies, equal radii relations

📐 Coordinate Patterns

• Coordinate Kill - Translate/rotate/scale, shoelace, determinant tricks
• Extremal Geometry Paths - Reflection method, minimum distance/path

🔄 Advanced Patterns

• Mass Points Templates - Standard lever setups, weighted Ceva
• 3D Projections & Sections - Areas/lengths via projection, prism/cube cross-sections
• Geometric Probability Patterns - Random chords/points on segments/regions

🎯 How to Use This Catalog

For Practice

1. Study each pattern - Understand the recognition cues
2. Practice templates - Work through the solution steps
3. Build recognition - Learn to spot patterns quickly

For Contests

1. Quick scan - Look for familiar patterns
2. Apply template - Use the standard approach
3. Adapt as needed - Modify for specific problem details

For Review

1. Identify gaps - Which patterns need more practice
2. Focus study - Work on weak pattern recognition
3. Build speed - Practice quick pattern identification

💡 Pro Tips

• Mark equalities on diagrams immediately
• Look for parallel lines - they create similar triangles
• Check for cyclicity - equal subtended angles often appear
• Use coordinate geometry when pure geometry gets messy
• Estimate first - eliminate obviously wrong answers

Next: Angle Chase Cycles → | Back to: Geometry Mastery Guide →