Exploring Analyic Geometry with Mathematica®

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Tangency Point on a Circle

tancirpt.html

Exploration

Show that if a line A x+B y+C=0 is tangent to a circle "tancirpt_1.gif" then the coordinates of the point of tangency are

"tancirpt_2.gif".

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

"tancirpt_3.gif"

Simplify to the desired form.

Map[Apart,p1]

"tancirpt_4.gif"


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