Transcript 6.1 Use Properties of Tangents

6.1
Use Properties of Tangents
Vocabulary
• A circle is the set of all points in a plane
that are equidistant from a given point
called the center of the circle.
• A radius is a segment whose endpoints
are the center and any point on the circle.
Vocabulary
• A chord is a segment whose endpoints
are on a circle.
• A diameter is a chord that contains the
center of the circle.
– The diameter is the longest chord a circle has.
Vocabulary
• A secant is a line that intersects a circle in
two points.
• A tangent is a line in the plane of a circle
that intersects the circle in exactly one
point, the point of tangency.
Vocabulary
• Theorem 6.1:
– 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.
Vocabulary
• Theorem 6.2:
– Tangent segments from a common external
point are congruent.
Example 1:
• Tell whether the line, ray, or segment is
best described as a radius, chord,
diameter, secant, or tangent of circle P.
Example 2:
• Use the diagram to find the given lengths.
Example 3:
• Tell how many common tangents the
circles have and draw them.
Example 4:
• RS is tangent to circle C at S and RT is
tangent to circle C at T.
– Find the value of x.
Example 5:
• In the diagram, BC is a radius of circle C.
Determine whether AB is tangent to circle
C. Explain.
Example 6:
• In the diagram, B is a point of tangency.
Find the radius r of circle C.
**Remember we know that the
radius is perpendicular to the
tangent**
This makes a RIGHT triangle!
So we can use
Pythagorean theorem to
solve for r.
Homework
P. 186 #1, 9-11, 12-20even