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?

Six circles around a central circle make a flower. Watch the flower
as you change the radii in this circle packing. Prove that with the
given ratios of the radii the petals touch and fit perfectly.

Square World

Age 16 to 18 Challenge Level:

$P$ is a point inside a square $ABCD$
such that $PA= 1$, $PB = 2$ and $PC = 3$.