# So Many Intersections

Geometry Level 3

Two non-intersecting circles in the plane $$\Gamma_1$$ and $$\Gamma_2$$ are drawn centered at points $$O_1$$ and $$O_2$$ respectively. A circle $$\Gamma_3$$ intersects $$\Gamma_1$$ at points $$X_1,X_2$$ and $$\Gamma_2$$ at points $$Y_1,Y_2.$$ Another circle $$\Gamma_4$$ intersects $$\Gamma_1$$ at points $$X_3, X_4$$ and $$\Gamma_2$$ at points $$Y_3, Y_4.$$ Suppose lines $$X_1X_2$$ and $$Y_1Y_2$$ intersect at $$K_1$$ and $$X_3X_4$$ and $$Y_3Y_4$$ intersect at $$K_2.$$ Find $$\angle K_1O_2O_1 + \angle O_2K_1K_2$$ in degrees.

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