The lengths of two parallel chords of a circle of radius 5 cm, are 6 cm and 8 cm in the same side of the centre. The distance between them is [SSC (10+2) 2014] |
A) 1.5 cm
B) 1 cm
C) 3 cm
D) 2 cm
Correct Answer: B
Solution :
Here, r = 5 cm, AB = 8 cm |
\[\therefore \] AN = NB = 4cm, CD = 6cm |
\[\therefore \] CM = MD = 3cm |
In \[\Delta ONB,\]\[O{{B}^{2}}=O{{N}^{2}}+N{{B}^{2}}\] |
\[{{5}^{2}}=O{{N}^{2}}+{{4}^{2}}\] |
\[\Rightarrow \] \[O{{N}^{2}}=25-16=9\] |
\[\Rightarrow \] \[ON=3cm\] |
In \[\Delta OMD,\]\[O{{D}^{2}}=O{{M}^{2}}+M{{D}^{2}}\] |
\[\Rightarrow \] \[{{5}^{2}}={{(ON+MN)}^{2}}+{{3}^{2}}\] |
\[\Rightarrow \] \[{{(3+MN)}^{2}}=25-9=16\] |
\[\Rightarrow \] \[3+MN=4\] |
\[\therefore \] \[MN=4-3=1\,cm\] |
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