Circle properties and circle theorems

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

Fixing It

Age

16 to 18

Challenge level

A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?
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?
problem

Circles in Circles

Age

16 to 18

Challenge level

This pattern of six circles contains three unit circles. Work out the radii of the other three circles and the relationship between them.
problem

Just Touching

Age

16 to 18

Challenge level

Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?
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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.