### Set Square

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?

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

### Biggest Bendy

Four rods are hinged at their ends to form a quadrilateral with fixed side lengths. Show that the quadrilateral has a maximum area when it is cyclic.

### Why do this problem?

It involves learners in visualisation and working with dynamic images and in conjecturing and proving. They have to select the mathematical information, methods and tools to use.

### Possible approach

You might use this problem in connection with work on circle theorems or later as an application and revision of previous work. You might accept the statement that a line joining the centres of two circles is perpendicular to the common chord or you might ask learners to prove this.

### Key questions

What stays invariant as the diagram changes?

What is changing?

What do you notice about the quadrilateral PQRS as the diagram changes?