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Ellipse Problem

Source: 2000 National High School Mathematics League, Exam One, Problem 10

March 10, 2020
conicsellipse

Problem Statement

In ellipse x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, FF is its left focal point, AA is its right vertex, BB is its upper vertex. If the eccentricity of the ellipse is 5−12\frac{\sqrt5-1}{2}, then ∠ABF=\angle ABF=________.
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