Product of Areas

In the diagram, there is a quadrilateral with perpendicular diagonals. Prove that the product of the areas of the shaded regions within the quadrilateral is equal to the product of the areas of the unshaded regions within the quadrilateral.

Difficulty level (1 very easy - 10 very hard): 3

Geometry -> Area Calculation Geometry -> Plane Geometry -> Triangles

Sources:

Young Mathematician Olympiad, 2017-2018, Final, Grades 5-6 Question 3

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