# Point of contact of circle an tangent

1. Mar 17, 2015

### sachin patil

I want to find out the co-ordinate of point of contact of tangent to a circle from external point when its center and radius are known. Please Help me . . .
Thank you in advance . . .

2. Mar 17, 2015

### Svein

This figure illustrates what you need to get ahead. The tangent and the radius to the tangent point meet at 90°. Thus: Draw a line from the given point to the center of the circle, find the midpoint and draw a circle with the line as diameter. The point where this circle intersects the given circle is the tangent point (as you can see from the figure, there are two tangent points).

3. Mar 17, 2015

### Mentallic

What happens when you simultaneously solve

$$y=mx+k$$
$$(x-a)^2+(y-b)^2=r^2$$

For x and y? They'll be in terms of the m,k,a,b,r constants, but it can be done.