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
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A tangent to a circle is perpendicular to the:
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Answer: Radius at the point of contact
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Angles subtended in the same segment of a circle are:
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Answer: Equal
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The sum of the interior angles of a quadrilateral is:
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Answer: 360°
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The sum of the interior angles of a triangle is:
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Answer: 180°
Practice Questions
Practise RMO questions on Euclidean Geometry. Answers are revealed after each question.
Start Practice →Frequently Asked Questions
What are the key concepts in Euclidean Geometry for RMO?
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.
Which formulae are important for Euclidean Geometry in RMO?
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.
How can I practise RMO Euclidean Geometry questions for free?
Practise free RMO Euclidean Geometry questions with instant answers and explanations on Safe Learning for Kids — no sign-up required.