Find the length of chord which is
at distance of 3 cm from the
Centre of circle.
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Step-by-step explanation:
The length of the chord of distance 3cm from its centre is 8cm.
Step-by-step explanation:
Given radius of the circle (AC) = 5 cm
AO =3 cm
Consider the triangle AOC, which is a right angled triangle.
By applying Pythagoras theorem, we can write,
\begin{gathered}\begin{array}{l}{\mathrm{AO}^{2}+\mathrm{OC}^{2}=\mathrm{AC}^{2}} \\ {3^{2}+\mathrm{OC}^{2}=5^{2}} \\ {9+\mathrm{OC}^{2}=25} \\ {\mathrm{OC}^{2}=16}\end{array}\end{gathered}
AO
2
+OC
2
=AC
2
3
2
+OC
2
=5
2
9+OC
2
=25
OC
2
=16
Taking square root,
OC = 4,
Therefore the length of the chord = 4 + 4 = 8 cm.
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