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AP/BP in terms of angles of ABC

Source: Netherlands - Dutch NMO 1972 p5

January 27, 2023
geometryratio

Problem Statement

Given is an acute-angled triangle ABCABC with angles α\alpha, β\beta and γ\gamma. On side ABAB lies a point PP such that the line connecting the feet of the perpendiculars from PP on ACAC and BCBC is parallel to ABAB. Express the ratio APBP\frac{AP}{BP} in terms of α\alpha and β\beta.
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