# Crazy tangents!

Geometry Level 5

$$O_1 , O_2 , O_3$$ are three circles which are tangent to each other and have radii $$R_1 , R_2 , R_3$$ and $$R_1 < R_2 < R_3$$

$$t_1 , t_2$$ are tangent to $$O_1$$ and $$O_2$$ other than at the tangent point of the two circles. They form $$\angle A$$

$$t_3 , t_4$$ are tangent to $$O_2$$ and $$O_3$$ other than at the tangent point of the two circles. They form $$\angle B$$

$$t_5 , t_6$$ are tangent to $$O_3$$ and $$O_1$$ other than at the tangent point of the two circles. They form $$\angle C$$

$$\sin A = \sqrt{2} -1$$ and $$B = 30^{ \circ }$$

Find the degree of $$\angle C$$.

Note: Image is for illustration only.

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