10.4. Given a triangle with sides $a, b, c$. On its sides as diameters, semicircles are constructed outward, resulting in a figure $F$ composed of the triangle and three semicircles. Find the diameter of $F$ (the diameter of a set in the plane is the greatest distance between its points).
Answer: $\frac{a+b+c}{2}$. Solution. See problem 9.4