MathDB
<BAN =<CAM wanted, symmedian , circumcircles, angle bisectors related

Source: 2011 Balkan Shortlist G2 BMO

April 3, 2020
geometrysymmedianequal anglescirclescircumcircleangle bisector

Problem Statement

Let ABCABC be a triangle and let OO be its circumcentre. The internal and external bisectrices of the angle BACBAC meet the line BCBC at points DD and EE, respectively. Let further MM and LL respectively denote the midpoints of the segments BCBC and DEDE. The circles ABCABC and ALOALO meet again at point NN. Show that the angles BANBAN and CAMCAM are equal.
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