Stage: 5 Challenge Level:
Consider the triangle $ABC$ as shown in the diagram. Use similar
triangles to show that if $\angle B = 2 \angle A$ then
To find integer solutions of this equation, consider the factors of
$a(a+c)=b^2$, and that $a$ and $a+c$ have no common factors, so $a$
and $a+c$ must be perfect squares. This will lead to a parametric
representation of $a$, $b$ and $c$ in terms of two parameters and
you can use this to generate the triples.