In ⊙ O , chord A B ¯ ∥ chord C D ¯ . Radius O E ¯ is perpendicular to A B ¯ and C D ¯ at points M and N , respectively. If O E = 13 , A B = 24 , and C D = 10 , then the distance from O to C D ¯ is greater than the distance from O to A B ¯ . Determine how much farther chord C D ¯ is from center O than chord A B ¯ is from center O ; that is, find M N .
Solution Summary: The Pythagorean theorem states that the distance from O to stackrel
In
⊙
O
, chord
A
B
¯
∥
chord
C
D
¯
. Radius
O
E
¯
is perpendicular to
A
B
¯
and
C
D
¯
at points
M
and
N
, respectively. If
O
E
=
13
,
A
B
=
24
, and
C
D
=
10
, then the distance from
O
to
C
D
¯
is greater than the distance from
O
to
A
B
¯
. Determine how much farther chord
C
D
¯
is from center
O
than chord
A
B
¯
is from center
O
; that is, find
M
N
.
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