Question

O is the centre of the circle .if AB = 8cm and OP = 3cm then find the radius of the circle.

Answer 1

See the figure.

AB is the chord.
OP is the perpendicular distance of chord AB from centre

OA is the radius = r
OP = 3cm
AP = 8/2 = 4cm

In the right angled triangle OAP
OA² = OP² + AP²
⇒ r² = 3² + 4²
⇒ r² = 25
⇒ r = √25 = 5cm

Radius of circle is 5cm.

Answer 2

See pic for reference.

OP is perpendicular to AB.
So, OP is also bisector of AB.
So, AP =4 cm

In right-angled triangle AOP,
$AO^{2} = OP^{2} + AP^{2}$
                    = $3^{2} + 4^{2}$
                    = 9+16
                    =25
So, AO = √25
             = 5 cm

The radius is 5 cm long.