Circle center : Cx,Cy

Circle radius : a

Point from which we need to draw a tangent line : Px,Py

I need the formula to find the two tangents (t1x, t1y) and (t2x,t2y) given all the above.


marked as duplicate by Leucippus, Alexander Gruber Apr 22 '18 at 18:25

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  • $\begingroup$ Hint $(x-x_c)^2+ (y-y_c)^2=a^2 $ you need to format using mathjax and show what you have done so far. $\endgroup$ – Karl Apr 22 '18 at 18:08
  • $\begingroup$ I understand the property of Pythagoras theorem. But that's not sufficient for me. I'm lost there. Is there any simpler solution using vector algebra or something to finding the equation of two lines and then solving equation of two straight lines twice to find the two tangents? I've to eventually write a program for this so it's better if it's optimal. $\endgroup$ – cegprakash Apr 22 '18 at 18:12
  • $\begingroup$ math.stackexchange.com/questions/543496/… this may help $\endgroup$ – Karl Apr 22 '18 at 18:21
  • $\begingroup$ Karl : I don't understand how (x−xc)2+(y−yc)2=a2 $\endgroup$ – cegprakash Apr 22 '18 at 18:24
  • $\begingroup$ it is the pythagoras' theorem. $\endgroup$ – Karl Apr 22 '18 at 18:27

Given that $$(x-x_c)^2+(y-y_c)^2=r^2$$ and a point $$P(x_0,y_0)$$ then the line through this point is given by $$y=m(x-x_0)+y_0$$ plug this in the equation of the circle to determine $m$

  • $\begingroup$ Karl : I don't understand how (x−xc)2+(y−yc)2=a2 $\endgroup$ – cegprakash Apr 22 '18 at 18:24
  • $\begingroup$ this is an equation of a circle with the centre $x_c,y_c$ $\endgroup$ – Dr. Sonnhard Graubner Apr 22 '18 at 18:25

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