Trigonometric Lengths

Geometry Level 3

In triangle ABC ABC, ACB=90\angle ACB = 90^\circ . Points A,D,E,A, D, E, and BB are consecutive points on side ABAB such that AD=DE=EB\overline{AD}=\overline{DE}=\overline{EB}. If there exists θ \theta such that CD=5cosθ \overline{CD} = 5 \cos \theta and CE=5sinθ\overline{CE} = 5 \sin \theta , what is AB2?\overline{AB}^2?

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