This document contains instructions and examples for measuring circles, segments, chords, and tangents. It includes the following examples:
1) Finding the length of a chord using the formula that the product of the parts of one chord equals the product of the parts of the other.
2) Solving a pair of equations involving a segment, radius, and variable part of a chord.
3) Explaining that the diameter of a circle bisects any chord perpendicular to it.
The document provides step-by-step workings for each example and problem.
4. .
6
x
4
(6+x) (6-x) = 4?4
36-x?=16
36-x?-36 = 16-36
-x?= -20
-x?/-1 = -20/-1
x? = 20
¡Ìx? = ¡Ì20
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
x? = 36
¡Ìx? = ¡Ì36
X = 6
