Ten squares form regular rings either with adjacent or opposite
vertices touching. Calculate the inner and outer radii of the rings
that surround the squares.
If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0
what can you say about the triangle?
One side of a triangle is divided into segments of length a and b
by the inscribed circle, with radius r. Prove that the area is:
Show that: angle $DBC$ + angle $DPC$ = angle $DQC$
Generalise this result.
N.B. This problem can be tackled in at least 8 different ways using different mathematics learnt in the last two years in school and earlier. The methods are essentially the same when viewed from a more advanced perspective.