by: Karen Caporino

Goals/objectives

- To construct a circle that is tangent to the radii 2 congruent circles

- To compare the area and circumference of the 2 tangent circles

- The circumference of the larger circle is twice the circumference of the smaller circle.
- The area of the larger circle to the smaller circle is proportional to the circumference of the larger to the smaller circle.

- Construct 2 congruent circles such that of each circle passes through the other circle's center.
- Construct another circle inside both of the larger circles that is tangent to both.

- The area of the larger circle is 4 times the area of the smaller circle
- The circumference of the larger circle is 2 times the circumference of the smaller circle.

- Given: AB = 2 (AC)

__Area__

area of Circle C = (AC)^{2}

area of Circle A = (AB)^{2}
^{
}= (2AC)^{2}

= 4 (AC)^{2}

- Therefore, the area of Circle A is 4 times
the area of Circle C.

circumference of Circle C = 2
(AC)

circumference of Circle A = 2
(AB)

= 2 (2 AC)

= 2*2 (AC)

Therefore, the circumference of Circle
A is 2 times the circumference of Circle C.

Click here to
see the construction.

Teaching strategies

Extensions