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第三届全国数学冬令营选拨赛试题第2题:设C_1、C_2是同心圆,C_2的半径是C_1的2倍。四边形A_1A_2A_3A_4内接于C_1,将A_4A_1延长交圆C_2于B_1,A_1A_2延长交圆C_2于B_2,A_2A_3延长交圆C_2于B_3,A_3A_4延长交圆C_2于B_4。试证:四边形B_1B_2B_3B_4的周长≥2×四边形A_1A_2A_3A_4的周长,并请确定等号成立的条件。本题可推广为: 设C_1、C_2是同心圆,C_2的半径是C_1的m(m>l)倍。 n(n≥3)边形A_1A_2…A_n内于C_1。将A_nA_1延长交圆C_2于B_1,
The third national mathematics winter camp election test question No. 2: Let C_1, C_2 be concentric circles, the radius of C_2 is 2 times that of C_1. The quadrilateral A_1A_2A_3A_4 is inscribed with C_1, and the A_4A_1 is extended into a circle C_2 with B_1. A_1A_2 extends the circle C_2 with B_2, A_2A_3 extends the circle C_2 with B_3, and A_3A_4 extends the circle C_2 with B_4. Testimony: The perimeter of the quadrilateral B_1B_2B_3B_4 ≥ 2 × the perimeter of the quadrilateral A_1A_2A_3A_4, and please confirm the condition that the equal sign is established. This question can be generalized as: Let C_1, C_2 be concentric circles, and the radius of C_2 be m_1(m>l) times of C_1. The n(n≥3) edge A_1A_2...A_n is inside C_1. Extend A_nA_1 to round C_2 to B_1,