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INAMO 2019 P3

Source: INAMO 2019 P3

July 2, 2019
Inamogeometry

Problem Statement

Given that ABCDABCD is a rectangle such that AD>ABAD > AB, where EE is on ADAD such that BE⊥ACBE \perp AC. Let MM be the intersection of ACAC and BEBE. Let the circumcircle of △ABE\triangle ABE intersects ACAC and BCBC at NN and FF. Moreover, let the circumcircle of △DNE\triangle DNE intersects CDCD at GG. Suppose FGFG intersects ABAB at PP. Prove that PM=PNPM = PN.
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