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A new problem posed by Lyndon Baker who has devised many NRICH problems over the years.

How would you design the tiering of seats in a stadium so that all spectators have a good view?

# Double Angle Triples

##### Stage: 5 Challenge Level:

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.