1. 10.3 – Apply Properties of Chords

2. In the same circle, or in congruent circles, two ___________ arcs are congruent iff their corresponding __________ are congruent.
minor
chords C B
then D A

3. If one chord is a _________________ _________ of another chord, then the first chord is the _________________.
perpendicular
bisector
diameter
and
then
is the diameter

4. If a ____________ of a circle is perpendicular to a chord, then the diameter ____________ the chord and its arc.
diameter
bisects
and the diameter
then

5. In the same circle, or in congruent circles, two chords are congruent iff they are _________________ from the _____________.
equidistant
center
and
then

6. 1. Find the given measure of the arc or chord. Explain your reasoning.=
105°
Congruent chords

7. 1. Find the given measure of the arc or chord. Explain your reasoning.
360 4 = =
90°
Congruent chords

8. 1. Find the given measure of the arc or chord. Explain your reasoning.
360 – 116 2 = =
122°
Congruent chords

9. 1. Find the given measure of the arc or chord. Explain your reasoning.= 6
Congruent arcs

10. Diameter bisects chord
1. Find the given measure of the arc or chord. Explain your reasoning. = 22
Diameter bisects chord

11. = 119° 119° Diameter bisects arc 61°
1. Find the given measure of the arc or chord. Explain your reasoning. =
119°
119°
Diameter bisects arc
61°

12. 50°
50° =
100°

13. 360 – 85 – 65 2 = =
105°

14. Find the value of x.
3x + 16 = 12x + 7
16 = 9x + 7
9 = 9x
1 = x

15. Find the value of x.
3x – 11 = x + 9
2x – 11 = 9
2x = 20
x = 10

16. _______________________
YES or NO
Reason:
_______________________
it is perpendicular and bisects

17. _______________________
YES or NO
Reason:
_______________________
it doesn’t bisect

18. 10.6 – Find Segment Lengths in Circles

19. If two chords intersect in the _______________ of a circle, then the ___________ of the lengths of the segments of one chord is equal to the product of the lengths of the segments o f the other chord.
interior
product

20. If two secant segments share the same endpoint ____________ a circle, then the ______________ of the lengths of one secant segment and its external segment equals the _____________ of the lengths of the other secant segment and its external segment.
outside
product
product

21. If a secant segment and a tangent segment share an endpoint ____________ a circle, then the product of the lengths of the secant segment and its external segment equals the ___________ of the length of the tangent segment.
outside
square

22. Find the value of x.
3  x = 9  5
3x = 45
x = 15

23. Find the value of x.
3x = 5(5+10)
3x = 75
x = 25

24. Find the value of x.
x2 = 2(2+16)
x2 = 36
x = 6

25. Find the value of x.
6  x = 8  3
6x = 24
x = 4

26. Find the value of x.
2  x = 5  5
2x = 25
x = 12.5

27. Find the value of x.
5(x + 5) = 6(6+4)
5x + 25 = 60
5x = 35
x = 7

28. Find the value of x.
x2 = 3(3+24)
x2 = 81
x = 9

29. Find the value of x.
2x  3x = 3  18
6x2 = 54
x2 = 9
x = 3

30. Find the value of x.
312 = 20(x + 20)
961 = 20x + 400
561 = 20x
28.05 = x

31. HW Problem 10.6 #6 8(x + 8) = 6(10+6) 8x + 64 = 96 8x = 32 x = 4 10.3
3-9, 12-14
3, 4, 6, 9, 13, 17
10.6 #6
8(x + 8) = 6(10+6)
8x + 64 = 96
8x = 32
x = 4