text: The group named for this shape is isomorphic to R mod Z. An inversion in the plane is defined based on one of these figures.
full_question: The group named for this shape is isomorphic to R mod Z. An inversion in the plane is defined based on one of these figures. The product of the two halves of a pair of segments which intersect in these shapes are equal, according to the power of a point theorem. One of these shapes in the complex plane is given by plotting the equation absolute value of z equals 5. Tangents to these shapes are always (*) perpendicular to the line through their center and the point of tangency. An ancient problem asks if it is possible to construct a square with area equal to a given one of these shapes. The intersection of the angle bisectors of a triangle gives the center of an inscribed one of these figures. For 10 points, identify these shapes, which have area equal to pi r-squared.
first_sentence: The group named for this shape is isomorphic to R mod Z. An inversion in the plane is defined based on one of these figures.
raw_answer: circles