By: Diana Brown
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 designated point.
Steps to creating a circle tangent to the two circles:
Draw two circles with the smaller circle being completely inside the larger circle
Construct a point on the larger circle by selecting the larger circle and go to construct point on circle.† Then construct a line from the center of the larger circle to this point.
Lets create a copy of the smaller circle with its center on the point of the larger circle created in step 2.† We can do this by selecting the radius of the smaller circle and the point on the larger circle and then go to construct and select circle by center + radius.
Construct a line segment from the center of the smaller circle to the intersection of the copied circle with the dashed line from the center, and construct its perpendicular bisector.
If we connect the intersection of the lines with the center of the smaller circle, we get an isosceles triangle. You can also see that the intersection of the lines is equidistant from the original circles. This distance is what we will use for the radius of the tangent circle.
Letís hide all of the dashed items to get a clear view of the two original circles and their tangent circle.
Click on the directly above picture for a script tool for tangent circles.
Letís explore what happens if we trace the center of the tangent circle while animating the point on the larger circle about the larger circle.
An ellipse is created.
Lets explore what happens if we do the same traces as above but we move the smaller circle to the outside of the larger circle.
The traces now create a hyperbola.
Click on the above picture to do your own explorations.