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.

×

Problem Loading...

Note Loading...

Set Loading...