find the length of a chord which is at distance of 4 cm from the centre of a circle whose radius is 5 cm.
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Given,
radius of circle OA= 5cm
distance between the centre and chord OB =4cm
we know that the perpendicular line drawn from the centre of the circle, bisects the chord in two equal parts.
by pythagoras theorem,
OA^2=OB^2+AC^2
5^2=4^2+AC^2
25=16+AC^2
25-16=AC^2
9=AC^2
AC=3
therefore, AB=2AC
=2×3
=6cm
radius of circle OA= 5cm
distance between the centre and chord OB =4cm
we know that the perpendicular line drawn from the centre of the circle, bisects the chord in two equal parts.
by pythagoras theorem,
OA^2=OB^2+AC^2
5^2=4^2+AC^2
25=16+AC^2
25-16=AC^2
9=AC^2
AC=3
therefore, AB=2AC
=2×3
=6cm
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