Join OB as shown in figure below:
OM = 5 cm
OM ⊥ AB and M is mid-point of AB,
MB = \(\frac 12\)AB
= \(\frac 12\) × 24
= 12 cm.
In right-angled triangle △OMB,
OB2 = OM2 + MB2
⇒ OB2 = 52 + 122
⇒ OB2 = 25 + 144
⇒ OB2 = 169
⇒ OB = 169 cm
OB = 13 cm.
As BP is tangent to circle at B, OB ⊥ BP.
In right-angled triangle △OBP,
OP2 = OB2 + BP2
⇒ OP2 = 132 + 202
⇒ OP2 = 169 + 400
⇒ OP2 = 569
⇒ OP = √569 cm
Hence, the length of OP = √569 cm.