A 30˚ angle inside an Equilateral Triangle

Geometry Level 3

Let \(P\) be the center of equilateral triangle \(ABC\). Points \(D\) and \(E\) are on \(\overline{BC}\) such that \(\angle DPE=30^\circ\). If \(BD=5\) and \(DE=7\), find \(EC\).

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