An angle with vertex A and measure α and a point P0 on one of its rays are given so that AP_0\equal{}2. Point P1 is chose on the other ray. The sequence of points P1,P2,P3,... is defined so that Pn lies on the segment AP_{n\minus{}2} and the triangle P_n P_{n\minus{}1} P_{n\minus{}2} is isosceles with P_n P_{n\minus{}1}\equal{}P_n P_{n\minus{}2} for all n≥2.
(a) Prove that for each value of α there is a unique point P1 for which the sequence P1,P2,...,Pn,... does not terminate.
(b) Suppose that the sequence P1,P2,... does not terminate and that the length of the polygonal line P0P1P2...Pk tends to 5 when k→∞. Compute the length of P0P1. geometry proposedgeometry