Tangent Circles
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
Conjecture/hypothesis/predictions
• 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.
Description of procedures
• 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.
Conclusions (Analysis using technology)
• 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

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.