Assignment #7 – Tangent Circles

Jackie Gammaro

This investigation involves finding a circle tangent to two given circles.  More specifically, given two circles and a point on the circles.  Construct a circle tangent to the two circles with one point of tangency being the designated point.

For this write-up, I am going to walk someone through the steps one would do to construct a tangent circle in GSP.

Step 1: Create a Circle, with Center A.

Step 2: Create another circle, with center B, inside circle A.

Step 3: Create a line AC, where C is a point on the circumference of circle A.

Step 4: Create a circle congruent to circle B centered at C.

Step 5:

(a) Label the intersection of where AC intersects circle C outside of circle A, call it point D.

(b) Construct segment BD.

Step 6:

(a) Find the midpoint of BD.

(b) Construct the line perpendicular to BD through the midpoint.

Step 7:

(a) Label the intersection of AC and the line perpendicular to BD, call it Point E.

(b) Point E is the center of the tangent circle, with radius EC.

Step 8:

Hide the following objects: Circle C, line AC, point D, line segment BD, it's midpoint, the line perpendicular to the midpoint.

You can see that Circle E is tangent to our given circles, circle A and circle B, with C as one point of tangency.

For further investigation, click on this link that allows you to explore more in GSP.

I also created a script tool for construction of tangent circles.  One can investigate many cases.  What if the circles are disjoint?  What if the circles intersect?  Where is the tangent circle? Click on this link to create two circles and itŐs tangent circles.