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Category: Geometry

Let-ABC-be-an-acute-angled-triangle-with-AC-BC-and-let-O-be-the-circumcenter-and-F-be-the-foot-of-altitude-through-C-Further-let-X-and-Y-be-the-feet-of-perpendiculars-dropped-from-A-and-B-respecti

Question Number 20545 by Tinkutara last updated on 23/Sep/17 LetABCbeanacuteangledtrianglewithACBCandletObethecircumcenterandFbethefootofaltitudethroughC.Further,letXandYbethefeetofperpendicularsdroppedfromAandBrespectivelyto(theextensionof)CO.ProvethatFYCA$$\mathrm{using}\:\mathrm{that}\:\angle\mathrm{CFY}\:=\:\angle\mathrm{CBY}\:=\:\angle\mathrm{CAF}. \