Definition. A circle that touches all three sides of a triangle is called the incircle of that triangle.

Theorem. The three angle bisectors of a triangle intersect at a single point. This point is the center of the triangle’s incircle.

Definition. A circle that touches one side of a triangle and the extensions of the other two sides is called an excircle.

Problems

How many excircles does a triangle have? Where are their centers located?
How can one construct the incircle and excircles of a triangle using a compass and straightedge?
The bisectors BB₁ and CC₁ of triangle ABC intersect at point M, and the bisectors B₁B₂ and C₁C₂ of triangle AB₁C₁ intersect at point N. Prove that the points A, M, and N lie on the same line.
The bisectors BD and CE of triangle ABC intersect at point O, and OD = OE. Must triangle ABC be isosceles?
The centers of the incircle and the circumcircle of a triangle coincide. Find the angles of the triangle.
Let O be the center of the incircle of triangle ABC. Find the angles ∠AOB, ∠BOC, and ∠AOC, if ∠A = 40°, ∠B = 70°.

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Properties of a Right-Angled Triangle

Circumcircle of a Triangle

Inscribed Quadrilateral

Geometry Warm-Up: Angles and Lines

Axioms and Postulates of Euclid

Morley's Triangle

Minimum and Maximum Problems in Geometry

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Where do you hold your classes?

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
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They will tell you about the pitfalls of exams and the most common mistakes, and explain how to avoid them

George Ionitsa

Founder &
Teacher of Maths and Coding

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