Problem

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Tags: perpendicular, geometry, angles



Consider the triangle $ABC$, with $\angle A= 90^o, \angle B = 30^o$, and $D$ is the foot of the altitude from $A$. Let the point $E \in (AD)$ such that $DE = 3AE$ and $F$ the foot of the perpendicular from $D$ to the line $BE$. a) Prove that $AF \perp FC$. b) Determine the measure of the angle $AFB$.