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 $x$ ?
Answer & explanation
Correct answer: option 3
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.