# Circles

Geometry Level 3

Let there be circles $$\Omega_1$$, $$\omega$$ and $$\Omega_2$$ with centers $$O_1$$, $$O_3$$ and $$O_2$$ respectively such that the lines $$O_1AA'$$ and $$O_1BB'$$ are tangent to circle $$\omega$$ at points $$A$$ and $$B$$ and also to circle $$\Omega_2$$ at $$A'$$ and $$B'$$. Besides, the lines $$O_2CC'$$ and $$O_2DD'$$ are also tangent to circle $$\omega$$ at points $$C$$ and $$D$$ and also to circle $$\Omega_1$$ at $$C'$$ and $$D'$$. The points $$A$$, $$B$$, $$C$$ and $$D$$ lie on the circle $$\omega$$ in that order. Find the value of $$\angle{O_3O_1A}$$ $$+$$ $$\angle{DO_2O_3}$$ $$-$$ $$\angle{BO_3C}$$.

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