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'Double Angle Triples' printed from http://nrich.maths.org/
Consider the triangle $ABC$ as shown in the diagram. Show that if
$\angle B = 2 \angle A$ then $b^2=a^2+ac$. Find integer solutions
of this equation (for example, $a=4$, $b=6$ and $c=5$) and hence
find examples of triangles with sides of integer lengths and one
angle twice another.