Question

The lengths of two parallel chords of a circle are $6$cm and $8$cm. If the smaller chord is at distance $4$cm from the centre, then the distance of the other chord from the centre is

• A. $5$cm
• B. $4$cm
• C. $3$cm
• D. $2$cm

Answer 1

The correct option is C $3$cm

In $\Delta$POB, $(OB{)}^2=(3{)}^2+(4{)}^2=9+16=25$
$\therefore OB=5=r$
In $\Delta$OQD, $(OQ{)}^2=(OD{)}^2-(QD{)}^2$
$=(5{)}^2-(4{)}^2=25-16=9$
$\therefore OQ=3cm$
Hence, the distance of the other chord from the centre
$=3cm$