If the tangent of the circle (X-2) 2 + (Y-3) 2 = 1 is made from point a (- 1,4), the length of the tangent is______ .
Because point a (- 1,4), let the tangent point be point B, connect the center O (2,3) and point B to get ob ⊥ AB, the radius of the circle is r = 1, and the hypotenuse Ao = (− 1 − 2) 2 + (4 − 3) 2 = 10. In the right triangle OAB, according to the Pythagorean theorem, the tangent length AB = (10) 2 − 12 = 3, so the answer is: 3
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