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Problem #210

Circle and his friend tangent

Consider two points A0 and A1 which are on a unit circle C centered at origin. Where point A0 is (1,0) and A1 is such that angle between positive direction of X-axis and radius vector through A1 is 1°.
The points Ai (i>=2) are obtained in the following way :
Consider vector Vi = A(i-1) - A(i-2), if A(i-1) and A(i-2) coincide take V as the tangent at A(i-1). Ai is obtained by intersection of circle with line which passes through Point A0 (1,0) and is parallel to Vi.

find the angle between X-axis and radius vector through An for n=123456789987654321. Give answer in degrees (Only output the integral part of the answer, if your answer is 19.23 enter 19 (19.0 will be wrong)).

Contributed by Aman Dubey

Solved by 23 users

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