204 Part 3: The Shape of the World
Lines and Angles ......................................................................................................................
Radii, diameters, and chords are line segments. They have endpoints that are either on the circle
or at the center of the circle. Lines that go on forever can also create angles that interact with the
circle.MATH TRAP
Remember that the center is not a point of the circle. The circle is points that are a set
distance from the center.A secant is a line that contains a chord. It is a line that intersects the circle in two distinct points.
A tangent is a line that touches the circle in exactly one point. Just the way tangent circles only
touched each other at one point, a tangent line only touches the circle at one point.
Secants and tangents also make angles on or around the circle. Two tangents, each of which
touches the circle in just one point, can cross outside the circle, making an angle. It will look like
an ice cream cone (the two tangents) holding a scoop of ice cream (the circle.) Two secants can
cross outside the circle to form the vertex of the angle, and then each intersects the circle twice,
dividing it into four arcs. Or a secant and a tangent can make an angle with its vertex outside the
circle, with the secant cutting the circle twice and the tangent just touching the side.DEFINITION
A secant is a line that intersects the circle it two different points. A tangent is a line
that only touches the circle at one point.Line FC is a secant. Line FA is a tangent.When these lines start making angles, there are a lot of angles and a lot of arcs that you can look
at, but the good news is that all three kinds of angles come down to the same measuring rule.
Let’s look at them one by one, starting with the angle formed by two secants.AFDC