Exploring Analyic Geometry with Mathematica®

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Circle Through Two Points, Center on Circle

tancir4.html

Exploration

Show that the radii of the two circles passing through the points (0,a) and (0,-a) with centers on the circle "tancir4_1.gif" are both given by

"tancir4_2.gif".

This is a special case of TangentCircles2D[{obj1,obj2},line | circle] where the two objects are points.

Approach

Two equations can be formed using the fact that points (0,a) and (0,-a) are on the circle. A third equation can be formed since the center is on a given circle. Solve three equations in three unknowns.

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

Solve three equations in three unknowns. The solutions with negative radii are invalid and discarded.

Clear[h,k,r];
ans1=Solve[{(0-h)^2+(a-k)^2==r^2,
            (0-h)^2+(-a-k)^2==r^2,
            h^2+k^2==r2^2},
           {h,k,r}]

"tancir4_3.gif"


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