SSC Sample Paper Mock Test-15 SSC CGL Tear-II Paper-1

AB and CD are two parallel chords on the opposite sides of the centre of the circle. If A5=10 cm, CD = 24 cm and the radius of the circle is 13 cm, the distance between the chords is

A) 17 cm

B) 15 cm

C) 16 cm

D) 18 cm

Correct Answer: A

Solution :

From O draw \[OL\bot AB\]and \[OM\bot CD.\] Join OA and OC.

AL \[=\frac{1}{2}\] AB = 5 cm, OA = 13 cm

\[O{{L}^{2}}=O{{A}^{2}}-A{{L}^{2}}={{(13)}^{2}}-{{5}^{2}}=(169-25)=144\] \[\Rightarrow \] \[OL=\sqrt{144}=12\,\,\text{cm}\]

Now, \[A{{B}^{2}}=O{{A}^{2}}+O{{B}^{2}}={{(12)}^{2}}+{{9}^{2}}=(144+81)=225\]and \[OC=13\,\,\text{cm}\]

\[\therefore \]\[O{{M}^{2}}=O{{C}^{2}}-C{{M}^{2}}={{(13)}^{2}}-{{(12)}^{2}}=(169-144)=25\]

\[\Rightarrow \] \[OM=\sqrt{25}=5\,\,\text{cm}\]

\[\therefore \] \[ML=OM+OL=(5+12)\,\,\text{cm}=17\,\,\text{cm}\]