Assignment 7: Tangent Circles
The problem for this assignment is as follows: Given
two circles and a point on one of the circles. Construct a circle
tangent to the two circles with one point of tangency being the
Below is a figure that represents the problem statment. One of the
circles is green with center G, and the other circle is blue and has
center Bl. Point T is the desired point of tangency on the green circle.
There are two different tangent circles that will
solve the problem. One solution is for the tangent circle to be inside
the green circle, and to have the red circle outside of it (Figure 2).
The second solution is for the tangent circle to again be inside the
green circle, and to have the red circle inside of it (Figure 3)
Click on each figure above to manipulate the geometry.
The method of construction is similar for both
solutions. 1. Construct a line (red) through points G & T (As
you can see from above the center (Bk) of the tangent circle is between
G & T). 2. Construct a circle with center T and same radius
as the blue circle (dashed blue circle). 3. This step is the
difference in the two solutions. For solution shown in Figure 2 create
a point (C) at the intersection of the (red) line and the new circle at
the point outside the green circle. For solution shown in Figure 3
create a point (C) at the intersection of
the (red) line and the new circle at the point inside the green
circle. 4. This step and the ones that follow are for both
solutions. Construct a segment between points C & Bl. 5.
Next, construct a perpendicular line (purple) throught the line created
in the previous step. 6.The point where the (purple) line
intersects the (red) line is the center of the (black) tangent circle.
As the point T is moved along the
circumference of the green circle, the center (Bk) of the tangent
circle will trace an ellipse or a hyperbola. Click
to experiment with tracing. Note: The two circles (green
& blue) can be moved and resized by manipulating their centers.
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