We know that the radius and tangent are perpendicular at their point of contact
In right triangle AOP
AO2 = OP2 + PA2
\(\Rightarrow\) (6.5)2 = (2.5)2 + PA2
\(\Rightarrow\) PA2 = 36
\(\Rightarrow\) PA = 6cm
Since, the perpendicular drawn from the center bisects the chord.
∴ PA = PB = 6cm
Now, AB = AP + PB = 6 + 6 = 12 cm
Hence, the length of the chord of the larger circle is 12cm.