Quadrilaterals

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
Favourite

Quad in Quad

Age

14 to 18

Challenge level

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
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?
problem
Favourite

Flexi Quads

Age

16 to 18

Challenge level

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?