Download Circles - Basic Terms

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NOTES: Circles - Introductory Terms
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DATE:
Circles - Basic Terms
Use Circle Q to comldete the.fi)llowing:
I) Name three (3) radii.
2) Name two (2) chords.
3) Name two (2) diameters.
4) Name a secant.
5) Name two (2) tangents.
E
G~o~leIFy
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NOTES: Circles -Arcs & CentralAngles
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Arcs & Central Angles of Circles
A circle has a total of 360°...
To understand angle relationships related to circles, the_[bllowing terms are required:
~e_.~ffr~AnN]e An angle with its vertex at the center of the circle.
Arc
An unbroken part of a circle...any two points on a circle are the endpoints of the
arc between them.
Like an angle, arc’s have a corresponding degree measure.
An arc measuring less than 180°.
Minor arcs are named usm~ the arc s e adpomts w~th an arched hat ... ex: AB
The measure of a minor arc is equal to the measure of its central angle. (mAB)
An arc measuring more than 180°, but less than 360°.
Major arcs are named for the endpoints and a point between them.., ex: ACB
The measure of a major arc is equal to 360° minus the measure of its minor arc.
An arc whose endpoints are on a diameter of the circle.
A semicircle also uses three letter notation.
A semicircle measures 180°.
ddjacentArcs Two arcs in the same circle with exactly one point in common (an endpoint).
Intercepted Are The arc formed by intersecting an angle with a circle (the arc "cut off" by an angle)
Use Circle Q to complete the folhm~ing.
1) Name two (2) central angles.
2) Name four (4) minor arcs.
3) Name four (4) major arcs.
4) Name two (2) semicircles.
5) Name two (2) minor arcs adjacent to AB.
6) Name one (1) major arc adjacent to AB. (Why isAl)l~ NO’r an answer?)
7) Name the arc intercepted by/_DQC.
8) Ifm/_AQD = 60°, then mAD =
and mABD =
9) IfmDBC = 220°, then mDC =
and mLDQC =
Geometry
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WORKSHEET: Circle Theorems - Chords
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The diameters of a given circle all intersect at the center.
Therefore, the center of a circle can be found by constructing two diameters.
Theorem In a circle, ~f a diameter is perpendicuhtr to a chord, then it bisects the
chord and its arc.
A chord that is the perpemlicular bisector of another chord is a diameter.
Draw a chord of this circle by first locating
two points on the circle (not a diameter).
Draw the perpendicular bisector of this chord
by first locating the midpoint of the chord.
This bisector is a diameter.
Repeat this process for another chord.
Where do the perpendicular bi sectors intersect?
Theorem In a circle or in congruent circles, ~vo chords are congruent ~f and only
they are equidistant from the center.
(The distance to a chord is &~fined as the petwendieular distance,)
Solve for x.
G
In a circle, all radii are congruent!
Can you find the radius of circle Q?
Theorem In a circle or congruent circles, two minor arcs are congruent O" and only
~[’their eorrespomling chords are congruent.
~
Draw three adjacent congruent arcs by:
Draw and label chord AB 3cm long.
Draw and label chord BC 3cm long
Draw and label chord CD 3cm long.
What can we conclude about arcs At3, BC, and C
Geometry
WORKSHEET: Circle Theorems
Inscribed Angl~s
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ln~’(ibgdA~g~ - an angle whose vertex is on the circle and whose sides are chords of
the circle.
Theorem If an angle is inscribed in a circle, then the measure of the angle equa[s
the measure of the intercepted arc.
Write an equation relating a and b in the
diagram.
Theorem If two inscribed angles intercept the same arc then the angles are
Draw two inscribed angles on this circle
that demonstrate this theorem.
Theorem If an inscribed angle qf a circle intercepts a semicircle, then the angle is a
Create a diagram to demonstrate this theorem / x,~
Th eo rem lf’a quadrilateral is inscribed in circle, then its opposite angles are
Create a diagram to demonstrate this theorem / ~
Find all lettered measures andjustiJ) holy you know.
120°
NAM£
For use wiih pages 595-682
The diameter of a circle is given. Find the radius,
1. d= 6in.
2. d= 24cm
3. d= 15ft
4. d = 9 in.
7. r= lOin.
8. r = 4.6 cm
The radius of a circle is given, Find the diameter,
6. r= 8ft
5. r= llcm
Match the notation with the term that best describes it.
9, D
A. Center
10. ~
B. Chord
11. CD
C, Diameter
12. AB
D. Radius
13. C
E. Point of tangency
t4. AD
<-->
1.5. AB
E Common external tangent
G. Common internal tangent
16. ~
H, Secant
E
Use the diagram at the right.
17. What are tile center and radius of
18. What are the center and radius of ®B?
19, Describe tile intersection of the two circles.
20. Describe all the common tangents of the two circles,
21. Are the two circles congruent? Explain,
Tell whether ~ is tangent to ®C, Explain your reasoning.
22.
A
23.
24. Baseba# Stadium Tbe shape of the outfield fence in a
baseball stadium is that of a quarter circle. If the distance
from home plate to the wail is 330 feet, what is the radius
of the entire circle? What is the diameter of the circle?
Geometry
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