In Fig. 8, O is t

We know that, tangent of the circle is perpendicular to the radius through the point of contact

∴ ∠ OPT = 90^o

Also, it is given in the question that:

OP = 5 cm

OT = 13 cm

Now, in right triangle OPT by using the Pythagoras theorem we have:

OP² + PT² = OT²

(5)² + PT² = (13)²

PT² = 144

PT = 12 cm

As radius of the circle are equal to each other

∴ OP = OQ = OE = 5 cm

Also, ET = OT – OE

= 13 – 5

= 8 cm

Let us now assume PA = x cm

∴ AT = (12 – x) cm

We know that, tangents of a circle drawn from an external point are equal

∴ PA = AE = x cm

Now, in right triangle Aet by using the Pythagoras theorem we have:

AE² + ET² = AT²

x² + (8)² = (12 – x)²

x² + 64 = 144 + x² – 24x

24x = 80

∴

Now, AB = AE + EB

= AE + AE

= 2 × AE

= 2x

Putting the value of x, we get:

= 6.67 cm

Hence, the length of the AB will be 6.67 cm