Transcript Chapter 10.3 Notes: Apply Properties of Chords

Chapter 10.3 Notes: Apply
Properties of Chords
Goal: You will use relationships of arcs and
chords in a circle.
• What is a chord?
– A chord is a segment with endpoints on a circle.
• Any chord divides the circle into two arcs.
• A diameter divides a circle into two semicircles.
• Any other chord divides a circle into a minor arc and
a major arc.
• Theorem 10.3:
In the same circle, or in congruent circles, two minor
arcs are congruent if and only if their corresponding
chords are congruent.
Ex.1: In the diagram, P  Q, FG  JK , and
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mJK  80 . Find mFG.
Ex.2: Use the diagram of
D.
a. If mAB  110 , find mBC.
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b. If mAC  150o , find mAB.
Bisecting Arcs
• Theorem 10.4:
If one chord is a perpendicular bisector of another
chord, then the first chord is a diameter.
• Theorem 10.5:
If a diameter of a circle is perpendicular to a chord,
then the diameter bisects the chord and its arc.
Ex.3: Use the diagram of E to find the length of
AC. Tell what theorem you used.
Ex.4: Find the measure of the indicated arc.
a. CD
c. CE
b. DE
• Theorem 10.6:
In the same circle, or in congruent circles, two
chords are congruent if and only if they are
equidistant from the center.
Ex.5: In the diagram of
C , QR = ST = 16. Find CU.
Ex.6: In the diagram in example 5, suppose ST = 32,
and CU = CV = 12. Find the given length.
a. QR
c. the radius of
b. QU
C
Ex.7: Use the diagram of C to find the length of
BF. Tell what theorem you used.
Ex.8: In the diagram of P, PV = PW, QR = 2x + 6,
and ST = 3x – 1. Find QR.
Ex.9: In R, AB  CD and mAB  108 .
Find mCD.
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