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\center{\texbf{Top 10 things to know about circles}}

  \begin{enumerate}
    \item A circle is the set of points in a plane that are
    equidistant from a given point $O$ called the center.
    \item The distance $r$ from the center is called the radius, 
     and the point $O$ is called the center. 
     Twice the radius is known as the diameter, $d = 2r$.
    \item  The angle a circle subtends from its center is a full
      angle, equal to $360^\circ$ or $2\pi$ radians.
    \item The perimeter $C$ of a circle is called the circumference, and
    is given by $C = 2\pi r = \pi d$.
    \item The area of a circle is given by $A = \pi r^2$.
    \item A central angle is an angle  with endpoints $A$ and $C$ located
    on a circle's circumference and vertex $O$ located at the circle's
    center.
    \item For an inscribed angle  and central angle  with the same
    endpoints,
    $$  \angle AOC = 2 \angle ABC $$
    \item A tangent to a circle at a point $p$ is perpendicular to the
    radius $OP$.
    \item The circumcircle is a triangle's circumscribed circle, i.e.,
    the unique circle that passes through each of the triangle's three
    vertices. The center $O$ of the circumcircle is called the
    circumcenter, and the circle's radius $R$ is called the
    circumradius. A triangle's three perpendicular bisectors (i.e. the
    line perpendicular to the side from the midpoint of the side)
    meet at $O$.
    \item The incircle is the inscribed circle of a triangle , i.e.,
the unique circle that is tangent to each of the triangle's three
sides. The center $I$ of the incircle is called the incenter, and the
radius $r$ of the circle is called the inradius.  The incenter is the
point of concurrence of the triangle's angle bisectors.
  \end{enumerate}
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