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Perpendicular Lines Generated by a Quadrilateral

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The centroid of a triangle is the intersection of the lines drawn from the vertices to the midpoints of the opposite sides.
The orthocenter of a triangle is the intersection of the altitudes.
Let ABCD be a quadrilateral. Let O be the intersection of AC and BD. Draw lines between the centroids of AOB and COD and the orthocenters of BOC and DOA. Those lines are perpendicular.
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