MathDB
Concurrency(little hard)

Source: Rioplatense Olympiad 2000

February 28, 2018
geometry

Problem Statement

Let ABCABC be a triangle with AB<ACAB < AC, let LL be midpoint of arc BCBC(the point AA is not in this arc) of the circumcircle ww(ABCABC). Let EE be a point in ACAC where AE=AB+AC2AE = \frac{AB + AC}{2}, the line ELEL intersects ww in PP. If MM and NN are the midpoints of ABAB and BCBC, respectively, prove that AL,BPAL, BP and MNMN are concurrents
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