A circle can be inscribed in a convex quadrilateral if and only if the angle bisectors of three of its angles intersect at one point.
A circle can be inscribed in a convex quadrilateral if and only if the sums of the lengths of its opposite sides are equal.
Problems
Determine the type of parallelogram into which a circle can be inscribed.
A circle is inscribed in an isosceles trapezoid. Prove that the lateral side of the trapezoid is equal to its midline.
Given a trapezoid into which a circle can be inscribed. Prove that circles constructed on the lateral sides as diameters touch each other.
Definition: A quadrilateral with two pairs of equal adjacent sides is called a kite (or deltoid).
a) Can a circle always be inscribed in a kite? b) Prove that one of the diagonals of a kite is its axis of symmetry.
Prove that if there exists a circle that touches all sides of a convex quadrilateral ABCD, and another circle that touches the extensions of all its sides, then the diagonals of such a quadrilateral are perpendicular.
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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 They will tell you about the pitfalls of exams and the most common mistakes, and explain how to avoid them
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