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CliffsStudySolver Geometry
The preceding figure shows that AC is a tangent to Circle W, with its point of tangency at R. Chord GN is actually a part of secant LM. A common tangent is a line tangent to two circles in the same plane. If it is an internal common tangent, it intersects the line segment that connects the centers of the two circles (whether or not that line segment is actually drawn) An external common tangent does not intersect the line segment connecting the two centers. Following are examples of both types. m
l R
M N external common tangent
Q
internal common tangent
Example Problems These problems show the answers and solutions. All problems refer to this diagram.
H D
F
G
J
K C
A
B E
1.
I
What is the name of the circle on the left? Answer: Circle A A circle is named by its center. In this case, the center is labeled A, so that names the circle.
2.
Name an internal common tangent. Answer: GI Since GI touches each circle at one point, it is their common tangent. Even though no line is drawn connecting the centers of the circles, if one were drawn, GI would intersect it. That’s what makes it an internal common tangent.
3.
Name all chords. Answer: JK and DE A chord has its endpoints on the circle. JK and DE are the only line segments to do this.
4.
Name all diameters. Answer: DE circle.
The diameter of a circle is its longest chord and contains the center of the