Quadrilaterals

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

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

Square Pair

Age

14 to 18

Challenge level

Explore the shape of a square after it is transformed by the action of a matrix.
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?
article
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.