Warm-Up Draw a circle with the following parts labeled: Center point , radius , and diameter . Warm-Up
Ra d i us Draw a circle with the following parts labeled:
Center point , radius , and diameter . Center A circle is the set of all coplanar points that are
equidistant from a fixed point on the plane. Center = fixed point Radius = equal distance Warm-Up
Ra d i us
Draw a circle with the following parts labeled: Center point , radius , and diameter . D i a m e t e r Center
A diameter consists of two radii, but thats not its definition. Can you guess why? Chord
Chord A chord is a segment whose endpoints are on a circle
Diameter Diameter A diameter is a chord
that intersects the center of the circle. Example 1 Lisa has a circular piece of cardboard with a 10-inch diameter. She wants to cut a 10inch by 2-inch rectangle from the circle.
She also wants to cut 10 square pieces that are 1 inch on each side. What information makes this scenario impossible? Secant
Secant A secant is a line that intersects a circle in two points. A secant line always contains a
chord Tangent Tangent A tangent is a line
that intersects a circle at exactly one point. The point of intersection is called the point of tangency
Example 2 Explain why the wheels on a train are closer to being tangent to the rails than a car tire to the road.
Example 3 Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of .
Properties of Tangents Objectives: 1. To define and use circle terminology 2. To use properties of tangents to a circle
Example 4 Draw two coplanar circles that intersect in a) two points, b) one point, c) no points and have the same center. Common Tangents
A line, ray, or segment that is tangent to two coplanar circles is called a common tangent. Example 5 Tell how many common tangents the circles
have and draw them all. Common Tangents, II Common tangents come in two flavors: Common Internal Tangent: Intersect the segment that
joins the centers of the circles Common External Tangent: Does not intersect the segment that joins the
centers of the circles Example 5, Revisited Determine whether the common tangents are internal or external.
Tangent Line Theorem In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle
at its endpoint on the circle. Circular Motion An interesting application of the Tangent Line Theorem
involves circular motion. A satellite, for example maintains its velocity in a direction tangent to its circular orbit. This velocity vector is perpendicular to
the force of gravity, which keeps the satellite in orbit. Example 6 The center of a circle has coordinates
(1, 2). The point (3, -1) lies on this circle. Find the slope of the tangent line at (3, -1).
6 4 2
5 -2 Example 7 Is tangent to ? Explain your reasoning.
Example 8 Point is a point of tangency. Find the radius of Example 9
Point is a point of tangency. Find the value of . Example 10 What must be true about tangent segments and ?
Congruent Tangents Theorem Tangent segments from a common external point are congruent.
Example 11 The points and are points of tangency. Find the value(s) of . Example 12 A circle has a radius of 6 inches. Two radii form a
central angle of 60. Tangent lines are drawn to the endpoints of each of the radii. How far from the center do the two tangent lines intersect?