chapter 10.1 notes: use properties of tangents goal: you will use properties of a tangent to a...
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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
a. b.
c. d.
.C
AC AB
DE��������������
AE�������������� �
Ex.2: Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of
a. b.
c. d.
.C
DC BD
DE AE�������������� �
Ex.3: Use the diagram to find the given lengths.
a. Radius of
b. Diameter of
c. Radius of
d. Diameter of
AA
BB
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, is a radius of Is tangent to
PT .P ST?P
Ex.6: In the diagram, B is a point of tangency. Find the radius of
• Theorem 10.2:
Tangent segments from a common external point are congruent.
.C
Ex.7: is tangent to at S and is tangent to
at T. Find the value of x.
Ex.8: is tangent to Find the value of r.
RS C RT
C
ST .Q
Ex.9: In is tangent at A and is tangent at B. Find x.
Ex.10: Is tangent to
,C DA DB
DE ?C
Ex.11: Find the value of x.