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:
Eight distinct proofs were given to this
problem by two students, Alex and Neil (Madras College) using
respectively sines, cosines, tangents, vectors, matrices,
coordinate geometry, complex numbers and pure geometry.