Question

In a circle of radius 5 cm PQ and RS are two prajallel chords of length 8 cm & 6 cm respectively lying onthe opposite sides of sides of center The distance between the chords is

• A. 1 cm
• B. 5 cm
• C. 6 cm
• D. 7 cm

Answer 1

The correct option is D 7 cm

In a circle, the perpendicular bisector from the centre to the mid point of the chord, forms a right angled triangle as shown in the figure.
Now, the perpendicular distance between the centre to the chord PQ is calculated as
$=>{OP}^2={OM}^2+{MP}^2$
$=>5^2={OM}^2+4^2$ (Since, MP is half of the chord PQ )
$=>OM=3cm$

Similarly, the perpendicular distance between the centre to the chord PS is calculated as
$=>{OR}^2={ON}^2+{NR}^2$
$=>5^2={ON}^2+3^2$ (Since, MP is half of the chord PQ )
$=>ON=4cm$
Since the chords are on either side of the centre, distance between the chords $=OM+ON=3+4=7cm$