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Circle definition
Circle: points in a plane that are a given distance (radius) from a given point (center).
Circle P P
Radius: center to a point on the circle
Interior & Exterior of a circle
Interior of a circle:
points inside the circle
Exterior of a circle:
points outside the circle
exterior interior
Lines & Segments that intersect a circle
A
G O B
F
E C
D
Chord: is a segment whose endpoints
lie on a circle.
Diameter: -a chord that contains the center
-connects two points on the circle and passes through the center
Secant: line that intersects a circle at two points
Tangent• A tangent to a circle is a line in the plane of the circle that
intersects the circle in exactly one point
• The point where a circle and a tangent intersect is the point of tangency A
Point B
B
Pairs of circles
Congruent Circles: two circles that have congruent radii
Concentric Circles: coplanar circles with the same center
Tangent Circles
Tangent Circles: coplanar circles that intersect at exactly one point
Internally tangent externally tangent
circles circles
Common Tangent
Common tangent: a line that is tangent to two circles
Common external common internal
tangents tangents
Example
is tangent to circle O. Radius is 5” and ED = 12”
Find the length of .
O
E D
Remember Pythagorean theorem (let = x)
= +
= 25 + 144
= 169
x=
x = 13
Example—Is there a tangent line?
Determine if there is a tangent line?
12 6
8
If there is a tangent then there must have been a right angle (in a right triangle). Test for a right angle.
+
144 36 + 64
144 100 so there is no right angle, no tangent line
Example
Find x.
130 x
Radius tangents (right angles)
Sum of the angles in a quadrilateral are 360
90 + 90 + 130 = 310
x = 360 - 310
x = 50