PPT-on-Segment-lengths-in-circles (2).ppt

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1. Segment Lengths in
Circles
Power Theorems

3. x = 9
x = 5
x = 6

4. A
B
A secant is a line that
intersects a circle at exactly
two points. (Every secant
contains a chord of the circle.)
T
A tangent is a line that intersects a circle at
exactly one point. This point is called the
point of tangency or point of contact.

5. Secant and Tangent Segments
A tangent segment is a point of a tangent line
between the point of contact and a point outside the
circle.
A secant segment is the part of a secant line that
joins a point outside the circle to the farther
intersection point of the secant and the circle.
T
B
Tangent segment
A
B
RAR is the secant segment.

6. The external part of a secant segment is the part
of a secant line that joins the outside point to the
nearer intersection point.
A
B
R
BR is the external part.

8. Theorem
When two chords intersect, the chords break
into segments that are equal when
multiplied.
A
B
C
D
X
XDCXXBAX 

9. Theorem
When chords intersect, the chords break
into segments that are equal when
multiplied.
A
B
C
D
X
XDCXXBAX 
8
3
4
6

10. Theorem
When chords intersect, the chords break
into segments that are equal when
multiplied.
A B
C
D
X
XDCXXBAX 
10
8
4
K

11. Theorem
When chords intersect, the chords break
into segments that are equal when
multiplied.
A B
C
D
X
XDCXXBAX 
10
8
4
K
5K

12. Theorem
When two secants intersect a circle, the
segments of the secants (the chord and
the whole secant ) are equal when
multiplied together. MQMPMOMN 

13. Theorem
When two secants intersect a circle, the
segments of the secants (the chord and
the whole secant ) are equal when
multiplied together. MQMPMOMN 
10
6
8
X
 
 648166
886106


X
X
SCALETO
DRAWNNOTPICTURE
1

14. Theorem
When two secants intersect a circle, the
segments of the secants (the chord and
the whole secant ) are equal when
multiplied together. MQMPMOMN 
10
6
8
X
 

4
832
64896
648166
886106





X
X
X
X
X
SCALETO
DRAWNNOTPICTURE
1

15. Theorem
A tangent and a secant
2
CDGDDF
CDCDGDGF



16. Theorem
A tangent and a secant
2
CDGDDF
CDCDGDDF


30
25 X

17. Theorem
A tangent and a secant
2
CDGDDF
CDCDGDDF


X
24
12

18. Theorem
A tangent and a secant
2
CDGDDF
CDCDGDDF


X
24
12
 
36
12432
14412576
121224
2




x
x
x
x

20. Example 4: Using Properties of Tangents
HK and HG are tangent to F. Find HG.
HK = HG
5a – 32 = 4 + 2a
3a – 32 = 4
2 segments tangent to
 from same ext. point
 segments .
Substitute 5a – 32 for
HK and 4 + 2a for HG.
Subtract 2a from both sides.
3a = 36
a = 12
HG = 4 + 2(12)
= 28
Add 32 to both sides.
Divide both sides by 3.
Substitute 12 for a.
Simplify.

21. Check It Out! Example 4a
RS and RT are tangent to Q. Find RS.
RS = RT
2 segments tangent to 
from same ext. point 
segments .
x = 8.4
x = 4x – 25.2
–3x = –25.2
= 2.1
Substitute 8.4 for x.
Simplify.
x
4
Substitute for RS and
x – 6.3 for RT.
Multiply both sides by 4.
Subtract 4x from both sides.
Divide both sides by –3.

22. x = 8 x = 8

23. x = 2

24. x = 5