设切点P(a, b), (a - 1)²+ b² = 1 (1)
圆心C(1, 0), r = 1
A(2, 1/2)
AP² + CP² = AC²
(a - 2)² + (b - 1/2)² + 1 = (1 - 2)² + (0 - 1/2)² (2)
(1) - (2): b = 4 - 2a
代入(1): 5a² - 18a + 16 = 0
(5a - 8)(a - 2) = 0
a = 8/5, P(8/5, 4/5), 切线(y - 4/5)/(1/2 - 4/5) = (x - 8/5)/(2 - 8/5), y = 2 - 3x/4
或
a = 2, P(2, 0), 切线:x = 2