Question

In the given figure O is the centre of the circle If $OP=3cm$ and radius of the circle is $5cm$ then find the length of AB

• A. $8cm$
• B. $6cm$
• C. $4cm$
• D. $2cm$

Answer 1

The correct option is A $8cm$

As AB is the chord. O is the centre of the circle. Since OP is the perpendicular drawn from O to AB as its distance, then OAP and OPB are both right angled triangles.
Now radius of the circle $OA=OB=5cm$
Using Pythagoras theorem, we have
$=>{OA}^2={OP}^2+{AP}^2$
$=>5^2=3^2+{AP}^2$
$=>{AP}^2=25-9=16$
$=AP=\sqrt{16}=4cm$
Similarly, $PB=4cm$
Hence, $AB=AP+PB=4+4=8cm$