129. A section of maximum area is made through the vertex of a right circular cone. It is known that the area of this section is twice the area of the axial section. Find the angle at the vertex of the axial section of the cone.
129. Any of the considered sections represents an isosceles triangle, the lateral sides of which are equal to the generatrix of the cone. Therefore, the section with the greatest area is the one where the sine of the angle at the vertex takes the greatest value. If the angle at the vertex of the axial section of the cone is acute, then the axial section has the greatest area. If this angle is obtuse, then the section with the greatest area is the right-angled triangle. Answer: $\frac{5}{6} \pi$.