In any triangle the midpoints of the sides, the base points of the altitudes and the midpoints of the altitude segments from intersection to vertex all lie on the same circle.
Diagram to accompany problem #28 of Heinrich Dörrie's [i]100 Great Problems of Elementary Mathematics[/i].
Step-by-step proof.
(Dependent upon:
Conditions for a quadrilateral inscribed in a circle.
)
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