200 Part 3: The Shape of the World
MATH IN THE PAST
Not every curve is a circle or part of a circle. Ancient mathematicians looked at the
different shapes that are seen when a cone is cut. If the cut goes straight across, you
see a circle, but if it slants a little, or a lot, you see different shapes. One of them is an
oval shape that mathematicians call an ellipse. It’s sort of a squashed circle.CHECK POINT
Complete each sentence.- An arc less than half a circle is a __ arc.
- The distance from the center point to any point on the circle is called the
__. - Two circles with the same center are __ circles.
- If two circles touch each other at just one point, the circles are __.
- An arc that is exactly half the circle is called a __.
Segments and Angles .............................................................................................................
When an angle is drawn so that its vertex is at the center of a circle, it’s called a central angle.
A central angle is an angle formed by two radii. The measure of a central angle is equal to the
measure of the arc between the endpoints of its sides, its intercepted arc. The measure of a
central angle is equal to the measure of its intercepted arc, and the measure of the arc is the
measure of the central angle that cuts it off. The two measurements are interchangeable.DEFINITION
A central angle is an angle with its vertex at the center of a circle whose sides are
radii.A chord is a line segment whose endpoints lie on the circle. The longer the chord, the closer it
will be to the center of the circle. Short segments will fit near the edge, but longer ones will
have to go closer to the center. The diameter is the longest chord of a circle. It passes through the
center of the circle. The diameter is twice as long as the radius.
When you draw a chord, you divide the circle into two portions, two arcs, usually a major arc
and a minor arc. You think of the minor arc as being the arc that belongs to that chord. If you