Tangential
Circles
Problem
Statement
Two larger circles with equal radii pass
through each other's centers. A smaller circle can be created inside the
overlapping region so that it is tangent to the other circles. (Tangent
means that the circles touch each other but do not cross over each other,
nor do they leave any gaps.) Compare the area and circumference
of the smaller circle to the area and circumference of the larger circle.
Investigation/Exploration of the Problem
For this problem, I did a few
quick calculations on a sheet of paper using an arbitrary figure for the
radius of the larger circles.
Here is a snapshot of what I came up with using Geometers Sketchpad:
Notice that the diameter of the
smaller circle is equal to the radius of the larger circles. Interesting don’t you
think? Well I did!
I digress…. Recall that
the formulas for area and circumference of a circle are as follows:
Look in the following math blurp
to see what I did with this information.
Now I truly feel that his would
be the case regardless of the length of the diameter of the larger
circles. Let’s
investigate using variables:
Author & Contact
If you find a flaw in my argument or have questions, feel free to contact
me!
