• # question_answer AB and CD are two parallel chords on the opposite sides of the centre of the circle. Lf AB=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

From O draw$OL\bot AB$  and $OM\bot CD.$ Join OA and OC. $AL=\frac{1}{2}AB=5\,\,cm,OA=13\,\,cm$ $O{{L}^{2}}=O{{A}^{2}}-A{{L}^{2}}$  $={{(13)}^{2}}-{{5}^{2}}=169-25=144$ $\Rightarrow$   $OL=\sqrt{144}=12\,\,cm$ Now, $CM=\frac{1}{2}\times CD=12\,\,cm$ and OC = 13 cm $\therefore$$O{{M}^{2}}=O{{C}^{2}}-C{{M}^{2}}={{(13)}^{2}}-{{(12)}^{2}}$ $=169-144=25$ $\Rightarrow$$OM=\sqrt{25}=5\,\,cm$ $\therefore$ML = OM +OL = (5+12) cm = 17 cm