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Trig bash or angle chase

Source: An Excursion in Mathematics

June 25, 2020
semicirclegeometryintersectionsstraight linestrigonometry

Problem Statement

On a semicircle with diameter ABAB and centre SS, points CC and DD are given such that point CC belongs to arc ADAD. Suppose ∠CSD=120∘\angle CSD = 120^\circ. Let EE be the point of intersection of the straight lines ACAC and BDBD and FF the point of intersection of the straight lines ADAD and BCBC. Prove that EF=3ABEF=\sqrt{3}AB.
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