First, I’ll just say what an amazing construction this was, with so many points of interest landing either exactly on the centre of a cell or exactly on a border between cells.

The points of interest are more than the three vertices of the scalene triangle, the nine points on the circle and the centre of the circle (marked with an X). There are also the circumcentre of the triangle and the orthocentre of the triangle. The Euler line is the line drawn through the circumcentre (the P of CATNEP in the grid) and the orthocentre (the G of NEARSIGHTED). (The centroid, or ‘centre’, of the triangle, incidentally, is one third of the way along the Euler line from the circumcentre to the orthocentre and does not have integer coordinates.) The centre of the circle (the X added at the end) is halfway between the circumcentre and the orthocentre.

The property of 50 that it is the sum of two squares in two different ways is exploited throughout this scenario. The circumcentre (P) is an x distance 5 and a y distance 5 from the two vertices of the triangle along the bottom and an x distance of 1 and a y distance of 7 from the vertex at the top. And when you look at the radii of the circle you will find that these linear distances are halved: 2.5/2.5 and 0.5/3.5.

Congratulations. Just a pity that Year 11/12 maths is needed to discover all these thematic shapes, points and lines, unless one can learn all about them in a hurry in time for the deadline! ]]>