### 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?

### 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.

### Strange Rectangle

ABCD is a rectangle and P, Q, R and S are moveable points on the edges dividing the edges in certain ratios. Strangely PQRS is always a cyclic quadrilateral and you can find the angles.

Combine the result from the problem Flexi Quad Areas that the area $A(Q) = {\textstyle{1\over 2}}d_1d_2\sin\theta$ with the definition of the scalar product and use the result from the problem Flexi Quads that the scalar product of the diagonals is constant.