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Terminology

Age 14 to 16 Challenge Level:
The green triangle is an isosceles triangle while the blue triangle is an equilateral triangle.

An isoceles triangle circumscribing and equilateral triangle with angles between the vertices of the equilateral triangle and isosceles triangle of a, b and c
Find $a$ in terms of $b$ and $c$.

What can you say about the triangles if $a = b = c$?