# Find coordinates of touching point of a tangent on a circle

I have a point '$a$' with known coordinates, from which I have drawn a tangent to a circle with center '$c$' which is also known. What is the best way of finding the coordinates of point '$b$', the touching point between the tangent and the circle? Here is a diagram: http://i.stack.imgur.com/gcKYn.jpg

Thanks,

David

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You have $(x-x_c)^2+(y-y_c)^2=r^2$ for the circle. You also have $(y-y_a)=m(x-x_a)$. $m=(x_c-x_a)/(y_c-y_a)$. Take the second equation, solve for $y$, plot it into the first equation, and solve for $x$.