Keith Jesell Cayabyab

Problem number 16

Problem: The diagonals of a quadrilateral ABCD intersect E; proved that the center of the circles circumscribed about the triangles AEB, BEC, DEA, are the vertices of a parallelogram.

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Procedure

Click the icon “polygon “to insert a quadrilateral ABCD.

Select the segment between two points icon to make a diagonal line AC, BD.

Intersect two objects, the diagonal AC, BD. The intersection would be point E.

Make circles which circumscribed the triangles AEB, BEC, CED, and DEA. Used circles through three points to construct.

Finally, connect the midpoints of a circle, point G, H, I, F which would be the vertices of a parallelogram.