proposed by Romania
Let ABCD be a cyclic quadrilateral and let HA, HB, HC, HD be the orthocenters of the triangles BCD, CDA, DAB and ABC respectively. Show that the quadrilaterals ABCD and HAHBHCHD are congruent.
solved by Leo Giugiuc (using complex numbers)
[solved , alternate solutions are welcome]
Let ABCD be a cyclic quadrilateral and let HA, HB, HC, HD be the orthocenters of the triangles BCD, CDA, DAB and ABC respectively. Show that the quadrilaterals ABCD and HAHBHCHD are congruent.
Θεωρούμε εγγράψιμο τετράπλευρο ABCD και τα ορθόκεντρα HA, HB, HC, HD των τριγώνων BCD, CDA, DAB και ABC αντίστοιχως. Να αποδείξετε οτι τα τετράπλευρα ABCD and HAHBHCHD είναι ίσα.
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