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Measure of an angle

Source: Paraguayan National Olympiad 2009, Level 3, Problem 2

August 31, 2014

Problem Statement

In a triangle ABCABC (∠BCA=90∘\angle{BCA} = 90^{\circ}), let DD be the intersection of ABAB with a circumference with diameter BCBC. Let FF be the intersection of ACAC with a line tangent to the circumference. If ∠CAB=46∘\angle{CAB} = 46^{\circ}, find the measure of ∠CFD\angle{CFD}.
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