212 Part 3: The Shape of the World
The Least You Need to Know
- A circle is the set of points at a fixed distance, called the radius, from a fixed
point, called the center. - A chord is a line segment that connects two points on the circle. A diameter is the
longest chord in a circle and passes through the center. - A secant is a line that contains a chord. A tangent touches a circle at just one
point. - A central angle has its vertex at the center of a circle and is equal to its inter-
cepted arc. An inscribed angle has its vertex on the circle and is equal to half its
intercepted arc. - When two chords intersect inside a circle, each pair of vertical angles formed is
equal to half the sum of the two intercepted arcs. - Angles formed by two secants, two tangents, or a tangent and a secant are equal
to half the difference of their intercepted arcs. - The equation of a circle with center (h,k) and radius r is (x – h)^2 + (y – k)^2 = r^2.
CHECK POINT- Write the equation of a circle with its center at the origin and a radius of 3
units. - Graph the circle represented by the equation x^2 + y^2 = 64.
- Find the center and radius of the circle represented by the equation (x – 8)^2 +
(x – 3)^2 = 49 - Write the equation of a circle with center (4,9) and radius of 2 units.
- Graph the circle represented by the equation (x – 8)^2 + (y – 3)^2 = 36.