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This lecture covers the proof of Exercise 5 in Analytical Geometry, focusing on the intersection of heights in a triangle. The instructor explains the notations used and demonstrates the step-by-step process to prove the exercise. The lecture emphasizes the application of trigonometry concepts to solve geometric problems, particularly in the context of triangle properties and heights. Various equations and formulas are presented to support the proof, showcasing the analytical approach to geometry problems. The lecture concludes with a detailed explanation of the coordinates and equations involved in the proof.