How to find what degree on a circle is tangent to a point outside of that circle?

Question

• I know the (x,y) of a point, P, outside of a circle.
• I know the (x,y) for the origin of a circle, O.
• I know the radius, r, of that circle.

How would I find what degree (e.g. 20 degrees, 270 degrees) is tangent to the point outside of the circle?

SOLUTION:

Hello Internet! So I ended up using the "circle form" formula at this reference http://www.ambrsoft.com/TrigoCalc/Circles2/CirclePoint/CirclePointDistance.htm to calculate the (x,y) coordinates of the point on the circle (radius not @ 0,0) Then I used: atan( y-Oy / x-Ox ) * 180/PI to get the 'degree' at that tangent point.

Answer 1

Sometimes a figure is worth a thousand words:

Can you draw the second tangent?

Can you calculate $d$?

At what angle does the tangent line strike the radius?

Can you use the Pythagorean Theorem?

Can you calculate $s$?