Course

Book 2. Olympiad Geometry Methods

Book 2. Olympiad Geometry Methods

  • 1. Advanced Angle Chasing
  • 2. Power of a Point
  • 3. Radical Axis
  • 4. Homothety and Spiral Similarity
  • 5. Inversion I: First Contact
  • 6. Ceva and Menelaus
  • 7. Area Method II
  • 8. Complete Quadrilaterals and Miquel Points
  • 9. Geometry with Coordinates and Vectors
  • 10. Mixed Problems II
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Theory Examples Practice Ladders

Chapters

Chapters

Chapter

Advanced Angle Chasing

The first module of Book 2 raises ordinary angle chasing to olympiad level: oriented angles modulo \(180^\circ\), cyclic quadrilaterals, tangents and chords, the angle between two circles, and more professional proof writing.
131 Problems
Theory Examples Practice

Chapter

Power of a Point

This module introduces one of the main tools of olympiad geometry: products of secant segments, tangent-secant, intersecting chords, equal powers, and first applications to proofs and ratios.
24 Problems
Theory Examples Practice

Chapter

Radical Axis

This module develops power of a point into a strong olympiad method: the radical axis of two circles, common chord, equal powers, radical center, and collinearity proofs through hidden equal powers.
24 Problems
Theory Examples Practice

Chapter

Homothety and Spiral Similarity

This module teaches students to recognise homothety and spiral similarity as sources of parallelism, collinearity, segment ratios, and hidden similar triangles.
24 Problems
Theory Examples Practice

Chapter

Inversion I: First Contact

This module introduces inversion as an olympiad tool: inverse points, images of lines and circles, angle preservation, tangencies, and first problems on choosing an inversion centre.
24 Problems
Theory Examples Practice

Chapter

Ceva and Menelaus

This module teaches students to use Ceva's and Menelaus' theorems to prove concurrence of lines, collinearity of points, and compute ratios on the sides of a triangle.
24 Problems
Theory Examples Practice

Chapter

Area Method II

This module develops the area method for olympiad problems: area and segment ratios, cevians, reconstruction of small areas, and a mass-points preview.
24 Problems
Theory Examples Practice

Chapter

Complete Quadrilaterals and Miquel Points

This module teaches students to recognise a complete quadrilateral, construct the Miquel point, and use it to prove concyclicity, angle equalities, and common points of circles.
24 Problems
Theory Examples Practice

Chapter

Geometry with Coordinates and Vectors

This module teaches how to choose convenient coordinates and use vectors, the dot product, line equations, and circle equations to prove geometric facts.
24 Problems
Theory Examples Practice

Chapter

Mixed Problems II

The final module of Book 2: the student chooses between angles, power of a point, radical axis, Ceva and Menelaus, areas, homothety, Miquel points, coordinates, and vectors.
24 Problems
Theory Examples Practice