Tangency Point on a Circle

tancirpt.html

Exploration

Show that if a line A x+B y+C=0 is tangent to a circle then the coordinates of the point of tangency are

.

Approach

The pole (point) of the line is the point of tangency.

Initialize

To initialize Descarta2D, select the input cell bracket and press SHIFT-Enter.

This initialization assumes that the Descarta2D software has been copied into one of the standard directories for AddOns which are on the Mathematica search path, $Path.

<<Descarta2D`

Solution

Create the line, circle and pole point.

Clear[A1,B1,C1,h,k,r];
p1=Point2D[
      l1=Line2D[A1,B1,C1],
      c1=Circle2D[{h,k},r]] //Simplify

Simplify to the desired form.

Map[Apart,p1]