Circles & intersecting lines

Let the touching point of the tangent line and the circle is (a,b)
Then (b/a)[(b-8)/(a-2)]=-1
b(b-8)=-a(a-2)
b^2-8b=-a^2+2a
a^2+b^2=2a+8b

The length of the tangent form the point (2, 8) to the circle x^2 + y^2 = 19
=√[(a-2)^2+(b-8)^2]
=√(a^2+b^2-4a-16b+68)
=√[a^2+b^2-2(2a+8b)+68]
=√[68-(a^2+b^2)]
=√(68-19) (Since a^2+b^2=19)
=7

2010-12-27 19:33:53 補充：
是中五程度