MathDB

The area of a convex quadrilateral is

S

, and the angle between the diagonals is

a

. On the sides of this quadrilateral, as on the bases, isosceles triangles with vertex angle equal to

\phi

, wherein two opposite triangles are located on the other side of the corresponding side of the quadrilateral than the quadrilateral itself, and the other two are located on the other side. Prove that the vertices of the constructed triangles, different from the vertices of the quadrilateral, serve as the vertices of a parallelogram. Find the area of this parallelogram.

Problem Statement