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Prove that two lines are perpendicular

Source: Rioplatense Olympiad 2013, Level 3, Problem 2

August 23, 2014
analytic geometrygraphing linesslopegeometrysimilar triangles

Problem Statement

Let ABCDABCD be a square, and let EE and FF be points in ABAB and BCBC respectively such that BE=BFBE=BF. In the triangle EBCEBC, let N be the foot of the altitude relative to ECEC. Let GG be the intersection between ADAD and the extension of the previously mentioned altitude. FGFG and ECEC intersect at point PP, and the lines NFNF and DCDC intersect at point TT. Prove that the line DPDP is perpendicular to the line BTBT.
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