Since chord CD and tangent at point T intersect each other at P ,
∴‌‌PC×PD=PT2 .........(1)
Since chord AB and tangent at point T intersect each other at P ,
∴‌‌PA×PB=PT2 ..........(2)
From (1) and (2),
PC×PD=PA×PB .........(3)
Given : CD=7.8‌cm;PD=5‌cm,PB= 4‌cm.
‌∴PA=PB+AB=4+AB,
‌PC=PD+CD=5+7.8=12.8‌cm.
Putting these values in eq. (3)
12.8×5‌=(4+AB)×4
⇒‌‌4+AB‌=‌

12.8×5

4

⇒‌‌4+AB‌=16
⇒‌‌AB‌=12‌cm.
‌ Hence, ‌‌‌AB‌=12‌cm.