Download 10-4 Chords, Secants, Tangents.notebook

10­4 Chords, Secants, Tangents.notebook
March 28, 2016
Tangent, Secant Lines and Chords
10­4 Chords, Secants, and Tangents
Point of Tangency
• I can name a chord, secant, and tangent line and their relationship with circles.
• I can describe the relationship between angles and chords when the angles are created inside, outside and on the circle.
• I can describe the relationship between opposite angles of inscribed quadrilaterals.
tangent line: intersects circle at exactly one point
radius
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secant line: intersects cir
If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. Mar 26­10:10 AM
Feb 28­7:20 AM
Circles can intersect each other 0, 1, or 2 times
Internally tangent circles
A line or segment that is tangent to two circles is called a common tangent.
There are two types: internal and external.
Internal common tangent
Concentric circles
External common tangent
Externally tangent circles
Feb 28­7:37 AM
An inscribed angle is: an angle whose vertex is on a circle
and whose sides contain chords of the circle. The arc that lies in the interior of an inscribed angle and has endpoints on the angle is called the intercepted arc of the angle.
Feb 28­7:42 AM
A
If an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc.
C
D
B
A
inscribed angle
intercepted arc
If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
C
B
D
Mar 28­3:25 PM
Mar 28­3:28 PM
1
10­4 Chords, Secants, Tangents.notebook
Find the measure of the indicated arc or angle.
B
March 28, 2016
you try
C
A
A
B
A
C
B
C
C
C
A
A
B
A
B
Mar 28­3:32 PM
C
B
Apr 14­4:59 PM
If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of a circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.
A
Can a circle be circumscribed about the quad?
Angle B is a right angle if and only if segment AC is a diameter of the circle.
C
B
A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.
F
E
D, E, F, and G lie on some circle, C, if and only if C
D
Mar 28­3:42 PM
Find x.
G
Mar 28­3:48 PM
If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intersected arc.
B
C
1
2
A
Mar 31­9:00 AM
Mar 28­3:48 PM
2
10­4 Chords, Secants, Tangents.notebook
March 28, 2016
If two lines intersect a circle, there are three places where the lines can intersect. Find the measure of angle 1.
b)
a)
1
1
in
c)
out
1
on
Mar 28­3:52 PM
Mar 28­3:55 PM
If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.
If two chords intersect in the interior of a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
B
A
1
C
D
P
1
2
C
2
A
Q
R
B
W
X
3
Z
Y
Mar 28­3:56 PM
Mar 28­3:59 PM
Find the measure of angle 1.
you try
Find the measure of angle 1.
a)
1
d)
c)
b)
f)
e)
1
1
1
1
1
Mar 28­4:00 PM
Apr 14­6:21 PM
3
10­4 Chords, Secants, Tangents.notebook
March 28, 2016
Find the value of x.
a)
b)
c)
Mar 31­11:04 AM
4