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Ratio of areas erected on right triangle

Source: Sharygin Finals 2017, Problem 9.6

August 3, 2017
ratiogeometryareas

Problem Statement

Let ABCABC be a right-angled triangle (∠C=90∘\angle C = 90^\circ) and DD be the midpoint of an altitude from C. The reflections of the line ABAB about ADAD and BDBD, respectively, meet at point FF. Find the ratio SABF:SABCS_{ABF}:S_{ABC}. Note: SαS_{\alpha} means the area of α\alpha.
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