Tangent Circles

BY: BRANDIE THRASHER

We are given the task to construct a circle that is tangent to two circles, given a point, in which that particular point is along the line of tangency to the circles.

We begin by constructing a circle

We then construct another circle (in this case inscribed in the larger circle)

Next, we construct a point on the outside circle and construct a line segment from the point to the center of circle A

We then construct a circle congruent to circle c centered at our point (F) created on circle A.

We now create a segment between points C and E and find its midpoint

Next, we will create perpendicular line to go through midpoint G. The point at which this line intersects line FA, will be labeled as H

From this construction, we will make a new circle with center H and point F. This circle will be the circle tangent to both circle A and C.

Here it is, all cleaned up!

When the given point is traced alongside the perpendicular line, another object is formed:

What are some conjectures we can come up with that can interpret what is happening?

Would we get the same resut if our tangent circle was not inscribed in the bigger circle?

Investigate more!

See the animation and script tool here