Suppose the diagonals of a quadrilateral ABCD meet at a point O; prove that the circumcentres of the 4 triangles OAB,OBC,OCD, and ODA form a parallelogram.
2026-03-28 16:56:59.1774717019
Circumcentre of triangles in a quadrilateral
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Note that any of the perpendicular bisector lines drawn will be used to determine the circum-centers of two adjacent triangles. For example, $L$ will be used to determined the circum-centers of $\triangle AOD$ and $\triangle DOC$.
The red line is parallel to the corresponding red dotted line. The same is true for the green colored pair.