Transcript Chapter 10.1 Notes: Use Properties of Tangents

Chapter 10.1 Notes: Use
Properties of Tangents
Goal: You will use properties of a tangent to a
circle.
Properties of a Circle
• 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 segment whose endpoints are the center and any
point on the circle is a radius.
• A chord is a segment whose endpoints are on a
circle.
• A diameter is a chord that contains the center of the
circle.
• 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, called the
point of tangency.
Ex.1: Tell whether the line, ray, or segment is best
described as a radius, chord, diameter, secant, or
tangent of C.
a. AC
b. AB
c. DE
d. AE
Ex.2: Tell whether the line, ray, or segment is best
described as a radius, chord, diameter, secant, or
tangent of C.
a. DC
b. BD
c. DE
d. AE
Ex.3: Use the diagram to find the given lengths.
a. Radius of
c. Radius of
A
b. Diameter of
A
d. Diameter of
B
B
Properties of Tangents
• Two circles can intersect in two points, one point, or
no points.
• Coplanar circles that intersect in one point are called
tangent circles.
• Coplanar circles that have a common center are
called concentric circles.
• A line, ray, or segment that is tangent to two
coplanar circles is called a common tangent.
Ex.4: Tell how many common tangents the circles
have and draw them.
a.
b.
c.
• Theorem 10.1:
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.
Ex.5: In the diagram, PT is a radius of
tangent to P ?
P. Is ST
Ex.6: In the diagram, B is a point of tangency. Find the
radius of C.
• Theorem 10.2:
Tangent segments from a common external point are
congruent.
Ex.7: RS is tangent to C at S and RT is tangent to
C at T. Find the value of x.
Ex.8: ST is tangent to
Q. Find the value of r.
Ex.9: In C , DA is tangent at A and DB is tangent at
B. Find x.
Ex.10: Is DE tangent to
C?
Ex.11: Find the value of x.