Intersecting CirclesGeometry Level 4
\(\Gamma_1\) is a circle with center \(O_1 \) and radius \(R_1\), \(\Gamma_2\) is a circle with center \(O_2\) and radius \(R_2\), and \(R_2 < R_1\). \(\Gamma_2\) has \(O_1\) on its circumference. \(O_1 O_2 \) intersect \(\Gamma_2\) again at \(A\). Circles \(\Gamma_1\) and \( \Gamma_2\) intersect at points \(B\) and \(C\) such that \( \angle CO_1B = 52 ^\circ \). \(D\) is a point on the circumference of \(\Gamma_1\) that is not contained within \( \Gamma_2\). The line \(DB\) intersects \(\Gamma_2\) at \(E\). What is the measure (in degrees) of the acute angle between lines \(DE\) and \(EA\)?