in a circle of a radius 10 cm , find the distance of a chord of length 16 cm from the center.
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Answer:
From the figure shown,
Radius=OA=10cm.
AB is the chord drawn with the length=16 cm.
We know,
perpendicular drawn from the centre of the circle to the chord ,bisects the chord
hence, C is the midpoint of AB.
Therefore,
AC=
2
AB
=
2
16
=8
So using Pythagorean Theorem:
OA
2
=OC
2
+AC
2
10
2
=OC
2
+8
2
100=OC
2
+64
OC
2
=36
OC=6cm
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