2.
SECANTS, TANGENTS AND ANGLES
• Up until now, we have discussed the tangents
and inscribed angles of certain circles.
• Now, we can discuss secants and the angles
created by them.
3.
SECANTS, TANGENTS AND ANGLES
• Like a tangent line, we judge a secant line by
the number of times it intersects the circle.
• THE NUMBER IS TWO!!!
• When two secant lines intersect inside a circle
then the angle formed is related to the arcs
they intercepts.
4.
SECANTS, TANGENTS AND ANGLES
• Theorem 14-8: If two secants or chords
intersect in the interior of a circle, then the
measure of an angle formed is one half the
sum of the measure of the arcs intercepted by
the angle and it’s vertical angle.
5.
SECANTS, TANGENTS AND ANGLES
• So let’s solve for the angles below.
A
C
B
D
X
40⁰
110⁰
50⁰
160⁰
6.
SECANTS, TANGENTS AND ANGLES
• What about this? Could you find ALL interior
angles?
A
C
B
D
X
35⁰
65⁰
7.
SECANTS, TANGENTS AND ANGLES
• Not only to secants interact with each other.
• Secants and tangents can intersect each other
too!
• What is the relationship here?
8.
SECANTS, TANGENTS AND ANGLES
• If a secant and tangent intersect at the point
of tangency, then the measure of the angles
will be half the measure of the arcs they
intersect.
9.
SECANTS, TANGENTS AND ANGLES
• Using the given information, find all missing
angles and arcs in the figure below.
120⁰
10.
SECANTS, TANGENTS AND ANGLES
• So we’ve dealt with angles on the interior of a
circle and ones directly on the circle…
• ..but what about those on the exterior of a
circle?
11.
SECANTS, TANGENTS AND ANGLES
• These angles can be formed of the
intersections of two secants, two tangents or
one of each.
12.
SECANTS, TANGENTS AND ANGLES
• Theorem 14-9: When any of these is the case,
the angle measure can be found by taking half
the difference of the two intercepted arcs.
13.
SECANTS, TANGENTS AND ANGLES
• Find the measure of angle P below.
P
30⁰
100⁰
14.
SECANTS, TANGENTS AND ANGLES
• Find the measure of angle P below.
P
30⁰
100⁰
M<P = 35
15.
SECANTS, TANGENTS AND ANGLES
• Find the measure of arc PO below…
P
30⁰
40⁰
O
16.
SECANTS, TANGENTS AND ANGLES
• Find the measure of arc PO below…
P
30⁰
40⁰
O
17.
SECANTS, TANGENTS AND ANGLES
• Today, you will need to use the information I
have given you in many ways!
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