draw projection from a point inside circle and find where it touches circle

Hi, I would like to draw projection from a point inside circle and find where it touches circle.(x4,y4) is my point inside circle.(x1-a)^2+(y1-a)^2=r^2 is my circle equation.I want to draw a tangent where it touches circle.Please help me with some example.

Thanks, Sita

Answer 1

[Image Analyst]

To draw a tangent line where it crosses the circle, you first need to know where it crosses. To know that you need more than just (x4,y4), you need to know the angle that you send out the line from that point. Obviously it will hit the circle at different places depending on the angle of the line emanating from that point.