Circle properties and circle theorems

problem

Triangle Incircle Iteration

Age

14 to 16

Challenge level

Keep constructing triangles in the incircle of the previous triangle. What happens?
problem

Cyclic Quad Jigsaw

Age

14 to 16

Challenge level

A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?
problem

Crescents and Triangles

Age

14 to 16

Challenge level

Can you find a relationship between the area of the crescents and the area of the triangle?
problem

Bicentric Quadrilaterals

Age

14 to 16

Challenge level

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
problem

Perfect Eclipse

Age

14 to 16

Challenge level

Use trigonometry to determine whether solar eclipses on earth can be perfect.
problem

Set Square

Age

16 to 18

Challenge level

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?
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The Cyclic Quadrilateral

This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.
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Incircles Explained

This article is about triangles in which the lengths of the sides and the radii of the inscribed circles are all whole numbers.
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Interacting With the Geometry of the Circle

Jennifer Piggott and Charlie Gilderdale describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions.
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Circle Theorems

This set of resources for teachers offers interactive environments which support work on properties of angles in circles at Key Stage 4.