In a circle with center $O$ and radius $5 \mathrm{~cm}, A B$ and $C D$ are two parallel chords of lengths $6 \mathrm{~cm}$ and $x \mathrm{~cm}$, respectively and the chords are on the opposite side of the centre $O$. The distance between the chords is $7 \mathrm{~cm}$. What is the value of $x$ ?

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Using Pythagoras Theorem,

OM = √\( { OA}^{2 } \) - \( {MA }^{2 } \)

= √\( { 5}^{2 } \) - \( {3}^{2 } \) = √16 = 4 cm.

= OM = 4cm

= ON = 7 - 4 = 3 cm

Again, Pyhtagoras theorem,

NC = √\( { OC}^{2 } \) - \( {ON }^{2 } \)

= √\( { 5}^{2 } \) - \( {3 }^{2 } \) = √16 = 4 cm.

DC = NC + DN

= DC = 4 + 4 = 8 cm

Therefore, DC is 8 cm.