To solve these problems, students should be familiar with:
Angle relationships formed by parallel lines and a transversal (corresponding, alternate, and co-interior angles).
Properties of angle bisectors and altitudes in triangles.
Internal angle sum formulas for polygons.
Basic geometric constructions involving squares and right triangles.
Angle properties in star polygons and composite figures.
Problems
Two parallel lines are intersected by a third line. Find the angle between the bisectors of the same-side internal angles.
Find the sum of the internal angles of: a) a quadrilateral; b) a convex n-gon.
In triangle ABC, ∠A = α. Find the angle between: a) the bisectors of angles B and C; b) the altitudes from vertices B and C (i.e., BM and CH). In part b), consider the cases where α < 90° and α > 90° separately.
Perfect (equilateral) triangles BCK and DCL are constructed externally on sides BC and CD of square ABCD. Prove that triangle AKL is also a perfect triangle.
On the extensions of the hypotenuse AB of right triangle ABC beyond points A and B, points K and M are placed such that AK = AC and BM = BC. Find ∠MCK.
Find the sum of the five angles at the tips of an irregular pentagram (five-pointed star).
We hold our classes online or on-site on Saturdays at our branch in Pimlico Academy, London. You can find our timetable here.
What do you need to start learning online?
For lessons you only need a computer or phone with a microphone, camera and Internet access. Wherever you are - in London, Nottingham, New York or Bali - online lessons will be at hand.
When can I take the trial lesson?
You can get acquainted with the school at any time convenient for you. To do this, just leave a request and sign up for a lesson.
What should I expect from the trial lesson?
The trial lesson is a 30-minute online session designed to get a sense of how your child approaches mathematical thinking and problem solving. (In practice, it often runs a bit longer if the student is engaged!)
We typically explore a range of fun and challenging problems drawn from competitions. We adapt the difficulty based on how the student responds, aiming to make it both accessible and stimulating.
After the session, we’ll have a quick conversation with the parent to share observations and suggest a personalised path forward.
I can't attend class, what should I do?
It is OK, it happens! Students have the opportunity to cancel a lesson up to 8 hours before the scheduled time without loss of payment. So you can reschedule it for a convenient time, and the teacher will have the opportunity to
I don't have much free time, will I have time to study?
Learning can take place at your own pace. We will select a convenient schedule and at any time we will help you change the schedule, take a break or adjust the program.
How long is one lesson?
All classes last 1 hour.
Meet our team
Our teachers will tell you how to prepare for exams, help you cope with difficult tasks and win the Olympiad They will tell you about the pitfalls of exams and the most common mistakes, and explain how to avoid them
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