area of quadr. independent of P, symmetric wrt midpoints - 1984 Kyiv City MO 8.1
Source:
July 15, 2021
geometryareafixedSymmetric
Problem Statement
Inside the convex quadrilateral lies the point . Reflect it symmetrically with respect to the midpoints of the sides of the quadrilateral and connect the obtained points so that they form a convex quadrilateral. Prove that the area of this quadrilateral does not depend on the choice of the point .