# Intersecting Circles

Geometry 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 $$EA$$?

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