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Byju's Answer
Standard IX
Mathematics
Chords Equidistant from Center Are Equal
Calculate the...
Question
Calculate the length of a chord which is at a distance of
12
cm
from the center of a circle of radius
13
cm
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Solution
From figure,
A
B
is the length of the chord,
and
A
C
=
B
C
(perpendicular from the center to the chord bisects the chord)
Using Pythagoras theorem in
△
A
O
C
⟹
A
O
2
=
A
C
2
+
O
C
2
⟹
13
2
=
A
C
2
+
12
2
⟹
A
C
2
=
169
−
144
⟹
A
C
2
=
25
⟹
A
C
=
5
Hence,
A
B
=
A
C
+
B
C
⟹
A
B
=
5
+
5
So, length of chord
A
B
=
10
cm
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