Πέμπτη, 12 Οκτωβρίου 2017

2000 JBMO problem 3 (ALB)

proposed by Albania


A half-circle of diameter ${EF }$  is placed on the side ${BC }$  of a triangle ${ABC }$  and it is tangent to the sides ${AB }$  and ${AC }$ in the points ${Q }$  and ${P }$  respectively. Prove that the intersection point ${K }$  between the lines ${EP }$  and ${F Q }$  lies on the altitude from ${A }$  of the triangle ${ABC }$.


posted in aops here

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