MathDB

2

Part of 2013 Junior Balkan MO

Problems(1)

JBMO 2013 Problem 2

Source: Proposed by Macedonia

6/23/2013
Let ABCABC be an acute-angled triangle with AB<ACAB<AC and let OO be the centre of its circumcircle ω\omega. Let DD be a point on the line segment BCBC such that ∠BAD=∠CAO\angle BAD = \angle CAO. Let EE be the second point of intersection of ω\omega and the line ADAD. If MM, NN and PP are the midpoints of the line segments BEBE, ODOD and ACAC, respectively, show that the points MM, NN and PP are collinear.
geometrycircumcircletrigonometryanalytic geometrygraphing linesslopeEuler