Originally Posted by

**wisterville** Hello,

I suggest two ways.

(1) (Cheating?) Use formulae.

"Given a circle C: (x-a)^2+(y-b)^2=r^2 and a point P(X, Y), what is the line L: (X-a)(x-a)+(Y-b)(y-b)=r^2?

(i) If P is on C, L is the line tangent to C at P.

(ii) If P is outside C, let M and N be the line tangent to C passing through P. If M meets C at the point A and N meets C at the point B, L is the line AB."

In this case, by (ii), 0x+(1+1)(y+1)=1 is the line joining the tangential points. x^2+(y+1)^2=1 and 2(y+1)=1 together gives the coordinates of the tangential points. Using (i), you can deduce the tangential lines at these points.