How to find the equation of a tangent line to a circle ( known radius) from a known point? And How to find the intersection point on the circle?

How to find the equation of a tangent line to a circle ( known radius) from a known point? And How to find the intersection point on the circle?

Answer 1

[Image Analyst]

This is not a MATLAB question - it's just analytical geometry formulas and algebra. Just draw it out and make sure you see the right angle between the center, the point off the circle, and the point on the circle. Then use the Pythagorean theorem.

[EDIT]

OK some more hints:

Let's say R is the radius, and (xr, yr) is on the circle, and (xc, yc) is the center of the circle, and (xp, yp) is the point away from and off the circle. So by the Pythagorean theorem

length1 = sqrt((xp-xr)^2 + (yp-yr)^2) % Length of side #1

length2 = sqrt((xp-xc)^2 + (yp-yc)^2) % Length of side #2

R^2 + length1^2 = length2^2 % The right triangle.

Plug in for length1 and length 2 :

R^2 + (xp-xr)^2 + (yp-yr)^2 = (xp-xc)^2 + (yp-yc)^2 % The right triangle.

Multiply out and cancel and combine terms and you'll be further along.

[Zarak kh]

Hello and thanks for your answer,

As you said I used mathematical and geometry formulation for my question as below:

I calculate the slope of the tangent line according to the fact that the slop of the tangent line is equal to derivation of the circle at that point. Then I have a point off the circle and the slope and I need to find the point on the circle. I also have the equation of the circle. so I have 2 equations and two unknown variables which are (xr, yr) and by solving them I get (xr, yr).

Regarding your answer as you wrote in the last line, you provide one equation with two unkown parameters which are (xr, yr). Should I add circle equation to your last equation?

[Image Analyst]

Try this web site for the formulas