Anne's theorem

In Euclidean geometry, Anne's theorem describes an equality of certain areas within a convex quadrilateral.

This theorem is named after the French mathematician Pierre-Léon Anne (1806–1850).

[1] The theorem is stated as follows: Let ABCD be a convex quadrilateral with diagonals AC and BD, that is not a parallelogram.

If the two sums of areas of opposite triangles are equal:

Moreover, the area identity of the theorem holds in this case for any inner point of the quadrilateral.