📐

Euclidean Geometry

Circle theorems, concurrency, collinearity, angle chasing, and triangle centres

Key Concepts
  • Similar triangles and the circle theorems
  • Power of a point for secants and tangents
  • Ceva's and Menelaus's theorems for concurrency and collinearity
  • Cyclic quadrilaterals unlock angle relationships
Important Formulae
Ceva's theorem (BD/DC)(CE/EA)(AF/FB) = 1 (concurrent cevians)
Menelaus's theorem (BD/DC)(CE/EA)(AF/FB) = −1 (collinear points)
Power of a point PA · PB = PC · PD
Quick Tips
  • Identify cyclic quadrilaterals early — they generate equal angles.
  • Angle chasing should usually be your first attempt.
Sample Practice Questions

  1. The sum of the interior angles of a triangle is:

    • 90°
    • 180°
    • 270°
    • 360°
    Show answer

    Answer: 180°

  2. In a cyclic quadrilateral, the sum of a pair of opposite angles is:

    • 90°
    • 180°
    • 270°
    • 360°
    Show answer

    Answer: 180°

  3. A tangent to a circle is perpendicular to the:

    • Diameter only
    • Radius at the point of contact
    • Chord
    • Tangent at another point
    Show answer

    Answer: Radius at the point of contact

  4. Angles subtended in the same segment of a circle are:

    • Equal
    • Supplementary
    • Complementary
    • Right angles
    Show answer

    Answer: Equal

Practise more questions →
Practice Questions

Practise RMO questions on Euclidean Geometry. Answers are revealed after each question.

Start Practice →
Geometry