MathDB

1

Part of 1988 Balkan MO

Problems(1)

another "strange" geometry problem of Bulgaria, but nice

Source: bmo 1988

4/23/2007
Let ABCABC be a triangle and let M,N,PM,N,P be points on the line BCBC such that AM,AN,APAM,AN,AP are the altitude, the angle bisector and the median of the triangle, respectively. It is known that [AMP][ABC]=14\frac{[AMP]}{[ABC]}=\frac{1}{4} and [ANP][ABC]=1−32\frac{[ANP]}{[ABC]}=1-\frac{\sqrt{3}}{2}. Find the angles of triangle ABCABC.
geometrytrigonometryratioangle bisectorgeometry proposed