Let ABCD be a cyclic quadrilateral, O be its circumcenter, P be a common points of its diagonals, and M,N be the midpoints of AB and CD respectively. A circle OPM meets for the second time segments AP and BP at points A1 and B1 respectively and a circle OPN meets for the second time segments CP and DP at points C1 and D1 respectively. Prove that the areas of quadrilaterals AA1B1B and CC1D1D are equal.
geometryequal areasareascyclic quadrilateral