Question

In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then distance OD is equal to

• A. 3 cm
• B. 4 cm
• C. 5 cm
• D. 3.5 cm

Answer 1

The correct option is A

3 cm

Here OD is bisecting AB, so AD = DB = 4 cm.

$\angle ODB={90}^{\circ }$ [Line through center that bisect the chord is perpendicular to chord]

So, $O{B}^2=O{D}^2+D{B}^2$ [$\because$ ODB is right angled triangle]
$O{D}^2=O{B}^2-D{B}^2$
$O{D}^2=(5{)}^2-(4{)}^2$ [OB is radius]
$O{D}^2=25-16$
$O{D}^2=9$
OD = 3 cm