$\mathrm{AB}$ and $\mathrm{CD}$ are two parallel chords on the opposite sides of the centre of the circle. If $\overline{\mathrm{AB}}=10 \mathrm{~cm}$, $\overline{\mathrm{CD}}=24 \mathrm{~cm}$ and the radius of the circle is $13 \mathrm{~cm}$, the distance between the chords is

Answer : Option A

Explanation :

OE ⊥ AB and OF ⊥ CD

AE = EB = 5 cm

CF = FD = 12 cm

AO = OC = 13 cm

From Δ AOE,

$\mathrm{OE}=\sqrt{13^{2}-5^{2}}=\sqrt{169-25}$

$=\sqrt{144}=12 \mathrm{~cm}$

From Δ COF,

$\mathrm{OF}=\sqrt{13^{2}-12^{2}}=\sqrt{25}=5 \mathrm{~cm}$

∴ EF = OE + OF = 17 cm