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The process of solving the eleventh problem of Jiangsu volume mathematics in the college entrance examination in 2003
Known AP=BP= 1, BP 1=PB? *? tanβ? =? tanβ?

p 1C = 1—BP 1 = 1—tanβ;

P2C=P 1C/? tanβ= 1/? tanβ— 1;

P2D=2—P2C=3— 1/? tanβ

P3D=? tanβ? *? P2D=3? tanβ— 1;

P3A= 1—P3D=2—3? tanβ

P4A=P3A/? tanβ=2/? tanβ—3;

Because P4 is between (1, 2), so

1 & lt; 2/? tanβ—3 & lt; 2

The range of tanβ is (2/5, 1/2).