Notes on 10-7

1. CIRCLES AND SEGMENT
MEASUREMENT
Jim Smith
JCHS
Section 10-7

2. a
b
c
d
THE PRODUCT OF
THE PARTS OF ONE
CHORD = THE PRODUCT
OF THE PARTS OF
THE OTHER CHORD
ab = cd

3. 7
x
4
5 7x = 20
7x= 20
7 7
X = 2.86
7x = 4(5)

4. .
6
x
4
(6+x) (6-x) = 4∙4
36-x²=16
36-x²-36 = 16-36
-x²= -20
-x²/-1 = -20/-1
x² = 20
√x² = √20
X = 4.47
Radius = 6, so
one part= 6+x
FOIL
and the other
part= 6-x
The diameter is
perpendicular to the
chord, so it bisects
the chord

5. The outside part of
segment AB x the
whole segment AB =
the outside part of
segment CB x the
whole segment CB
A
B
C

6. 5
7
15
x
Outside x Whole = Outside x Whole
5(x+5) = 7(15+7)
little+little = big
5x+25 = 7(22)
5x+25 = 154
5x = 129
X = 25.8

7. x
4
9
Tangent (the
outside is also
the whole)
Outside x Whole = Outside x Whole
x∙x = 4∙9
We know the whole so
we don’t need to add
the little parts
x² = 36
√x² = √36
X = 6

8. TRY THESE
8
5
7
X
3
X
5
14
1 2

9. 1) 7X = 8(5)
7X = 40
X = 40/7
X = 5.71
2) 3(X+3) = 5(14)
3X+9 = 70
3X+9-9 = 70-9
3X = 61
X = 61/3
X = 20.33