Properties of Circles
In the above diagram, circles and are both externally tangent to each other and inscribed in circle The radius of circle is the radius of circle is and the radius of circle is What is the sum of the lengths of and
Note: The above diagram is not drawn to scale.
Consider two circles with radius and respectively. If denotes the distance between the circle centers, and the number of lines that are tangent to both circles is what is the range of ?
Consider two fixed circles with different radii as shown in the above diagram. If the distance between their centers, denoted is then the two circles become externally tangent to each other. If the smaller circle becomes inscribed in the larger one. What is the radius of the larger circle?
In the above diagram, is the center of the circle and the length of is What is the length of
The above partial yin yang symbol is created from a large semicircle with radius by removing one semicircle with radius on the left and adding one semicircle with radius on the right. What is the circumference of the symbol?