A point O is chosen inside the square ABCD. The square A′B′C′D′ is the image of the square ABCD under the homothety with center at point O and coefficient k>1 (points A′,B′,C′,D′ are images of points A,B,C,D respectively). Prove that the sum of the areas of the quadrilaterals A′ABB′ and C′CDD′ is equal to the sum of the areas quadrilaterals B′BCC′ and D′DAA′. geometryhomothetysquareareas