Download Practice 10-3 and 10-4 10

NAME
10
DATE
PERIOD
SCORE
Practice 10-3 and 10-4
Advanced Geometry
Arcs and Chords Points on a circle determine both chords and arcs. Several properties are related to points on a circle.
In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
Exercises
ALGEBRA Find the value of x in each circle.
1.
2.
3.
6.
7.
4.
8. ⨀M ≅ ⨀P
5.
Diameters and Chords
• In a circle, if a diameter (or radius) is perpendicular to a chord,
then it bisects the chord and its arc.
• In a circle, the perpendicular bisector of a chord is the diameter (or
radius).
• In a circle or in congruent circles, two chords are congruent if and
only if they are equidistant from the center.
If ̅̅̅̅̅ ⊥ ̅̅̅̅ , then ̅̅̅̅ ≅ ̅̅̅̅ and ̂ ≅
̂.
If OX = OY, then ̅̅̅̅ ≅ ̅̅̅̅.
If ̅̅̅̅ ≅ ̅̅̅̅, then ̅̅̅̅ and ̅̅̅̅ are equidistant from point O.
Exercises
In ⨀P, the radius is 13 and RS = 24. Find each measure.
9. RT
̂
12. m𝐷𝐸
10. PT
11. TQ
Chapter 10
̂ = 90.
In ⨀A, the diameter is 12, CD = 8, and m𝑪𝑫
Find each measure.
13. FD
14. AF
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NAME _____________________________________________ DATE ____________________________ PERIOD _____________
16. In ⨀Q, ̅̅̅̅ ≅ ̅̅̅̅, GQ = x + 5 and
EQ = 3x – 6. What is x?
15. In ⨀R, TS = 21 and
UV = 3x. What is x?
Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose
sides contain chords of the circle. In ⨀G, minor arc ̂ is the intercepted arc for inscribed
angle ∠DEF.
Inscribed Angle
Theorem
If an angle is inscribed in a circle, then the measure of the angle
equals one-half the measure of its intercepted arc.
If two inscribed angles intercept the same arc or congruent arcs, then the angles are congruent.
Find each measure.
17. m ̂
19. m̂
18. m∠N
ALGEBRA Find each measure.
20. m∠U
21. m∠A
22. m∠T
23. m∠C
24. x
25. x
26. m∠W
Chapter 10
27 m∠T
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Glencoe Geometry