Question

In a circle of radius $13$cm, $PQ$ and $RS$ are two parallel chords of length $24$cm and l0cm respectively. The chords are on the same side of the centre then the distance between the chords is?

• A. $7$cm
• B. $12$cm
• C. $5$cm
• D. $10$cm

Answer 1

The correct option is A $7$cm

$OP=OR=13cm,PQ=24cm$ and $RS=10cm$

$PM=12cm$ and $RN=5cm$ [perpendicular from the centre bisects the chord]

In right angled triangle OMP and ONR ,by pythogoras theorem

${OP}^2={OM}^2+{MP}^2$

$OM=\sqrt{{OP}^2-{MP}^2}$

$OM=\sqrt{{13}^2-{12}^2}$

$OM=5cm$

${OR}^2={ON}^2+{RN}^2$

$ON=\sqrt{{OR}^2-{RN}^2}$

$ON=\sqrt{{13}^2-5^2}$

$OM=12cm$

$MN=ON-OM$

$MN=12-5$

$MN=7cm$

Therefore distance between the chords is $7cm$

option A is the answer.