A point P is selected anywhere inside an equilateral triangle. What
can you say about the sum of the perpendicular distances from P to
the sides of the triangle? Can you prove your conjecture?
What is the area of the quadrilateral APOQ? Working on the building
blocks will give you some insights that may help you to work it
Six circular discs are packed in different-shaped boxes so that the
discs touch their neighbours and the sides of the box. Can you put
the boxes in order according to the areas of their bases?
The trick with this question was not to make life difficult by
working values out. As a consequence some of you managed much more
elegant solutions than others. Here is an example based on that
offered by Shu Cao (very well done). Jeongmin Lee, Rebecca Bartram
(The Mount School, York) and Andrei Lazanu (School 205, Bucharest)
should also be congratulated.