The length of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at a distance of 4 cm from the centre, then the distance of the other chord from the centre is [SSC (10+2) 2013] |
A) 5 cm
B) 6 cm
C) 4 cm
D) 3 cm
Correct Answer: D
Solution :
Length of smaller chord be 6 cm. |
\[\therefore \] \[MB=3\,cm\,\]and \[OM=4\,cm\] |
\[\therefore \] In \[\Delta OMB,\]using Pythagoras theorem |
\[O{{B}^{2}}=O{{M}^{2}}+M{{B}^{2}}\] |
\[=9+16=25\] |
\[\Rightarrow \] \[OB=5\,cm\] [radius of the circle] |
\[\therefore \] \[OD=5\,cm\] |
and \[ND=\frac{CD}{2}=\frac{8}{2}=4\,cm\] |
\[\therefore \] In \[\Delta OND,\]using Pythagoras theorem |
\[O{{N}^{2}}=O{{D}^{2}}-N{{D}^{2}}\] |
\[=25-16=9\] |
\[\Rightarrow \] \[ON=3\,cm\] |
Distance = 3 cm |
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