4) The radius of a circle is
15cm. The distance of
centre O from M; the
B
midpoint of chord AB is
M
9 cm. Find the length of
A
chord AB
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The radius of a circle is given as 15 cm and chord AB subtends an angle of 131
∘
at the centre C of the circle.Using trigonometry ,calculate :
(i) the length of AB ;
(ii) the distance of AB from the centre C
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Answer
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Given r=15
∠AOB=13.1
AB=x
AC=CB=
2
x
∠AOC=65.5
o
sin65.5=
2×15
x
As sin65.5=0.909
x=0.909×30=27.27
∴ length of AB=27.27
OC=cos65−5×15
=0.414×15
OC=6.21cm
∴ length of chord AB=27.27cm
distance between centre and the chord is 6.21 cm.
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