Extra geometry III
Let D be a point inside an acute angled triangle ABC. Show that:
(DA)(DB)(AB) + (DB)(DC)(BC) + (DC)(DA)(CA) &ge (AB)(BC)(CA)
with equality if and only if D is the orthocentre of ABC.
(DA)(DB)(AB) + (DB)(DC)(BC) + (DC)(DA)(CA) &ge (AB)(BC)(CA)
with equality if and only if D is the orthocentre of ABC.
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