Segments of Circles Students will be able to
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GHSegments of Circles_notes(complete).notebook April 13, 2016 Segments of Circles 10.3 Arcs and Chords 10.5 Tangents 10.7 Special Segments in a Circle Students will be able to . . . • recognize and use relationships between arcs and chords. • recognize and use relationships between arcs, chords, and diameters. • use properties of tangents • solve problems involving circumscribed polygons • find measures of segments that intersect in the interior of a circle. • find measures of segments that intersect in the exterior of a circle.
Transcript of Segments of Circles Students will be able to
GHSegments of Circles_notes(complete).notebook April 13, 2016
Segments of Circles
10.3 Arcs and Chords
10.5 Tangents
10.7 Special Segments in a Circle
Students will be able to . . .
• recognize and use relationships between arcs and chords.
• recognize and use relationships between arcs, chords, and diameters.
• use properties of tangents
• solve problems involving circumscribed polygons
• find measures of segments that intersect in the interior of a circle.
• find measures of segments that intersect in the exterior of a circle.
GHSegments of Circles_notes(complete).notebook April 13, 2016
C
X
B
Y
ZA
In the same circle or congruent circles (equal radii), two minor arcs are congruent if and only if their corresponding chords are congruent.
If a diameter (or part of a diameter) of a circle is perpendicular to a chord, then it bisects the chord and its arc.
C
X
B
Y
Z C
X
B
Y
Z
L M
N
P
What is the given information in this picture?
GHSegments of Circles_notes(complete).notebook April 13, 2016
Chords which are equidistant from the center are congruent.
Congruent chords are equidistant from the center.
A radius can be added to create a right triangle to aid in solving a problem.
Example In P, JK = 10 and mJLK = 134o.
Find each measure.
(a) mJL
(b) PQ
Hint: Draw a radius to form a right triangle.
GHSegments of Circles_notes(complete).notebook April 13, 2016
Tangent Line that touches exactly one point on the circle (does not go inside the circle)
Radius is perpendicular to the tangent at the point of tangency.
Use the Converse of Pythagorean Theorem to prove LM is or is not tangent to K.
Example
Find x. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth if necessary.
Example
Find x. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth if necessary.
GHSegments of Circles_notes(complete).notebook April 13, 2016
If two segments from the same exterior point are tangent to a circle, then they are congruent.
Given AB and CB are tangent to D.
Example
AC and BC are tangent to Z. Show how to find the value of x.
Example
Triangle PQR circumscribes the circle. Find x, then find the perimeter.
GHSegments of Circles_notes(complete).notebook April 13, 2016
Special Segments
(a) Segments which intersect inside the circle (not at the center).
a
bc
d
Product of the segments of one chord
Product of the segments of the other chord
=
Example Find x.
GHSegments of Circles_notes(complete).notebook April 13, 2016
(b) Segments which intersect outside the circle.
A
B
C
DE
Part of segment outside circle
Total segment length
Part of other segment outside circle
Total other segment length
=
Examples Find x.
GHSegments of Circles_notes(complete).notebook April 13, 2016
Segments of Circles Practice
2.1.
3. 4.
Find the value of x in each circle.
The radius of N is 18, NK = 9, and mDE = 120. Find each measure.
mGE
m HNE
m HEN
HN
5.
6.
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8.
Find x. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth if necessary.
9. 10.
GHSegments of Circles_notes(complete).notebook April 13, 2016
For each figure, find x. Then find the perimeter.
11. 12.
Find x. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth if necessary.
13. 14.
16.
17. 18.
15.
