Given:

AP = 10 cm

OA = 6 cm

OB = 3 cm

Property : The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.

By above property, ∆PAO is right-angled at ∠PAO (i.e., ∠PAO = 90°) and ∆PBO is right-angled at ∠PBO (i.e., ∠PBO = 90°).

Therefore by Pythagoras theorem in ∆PAO,

OP² = OA² + AP²

⇒ OP² = 6² + 10²

⇒ OP² = 36 + 100

⇒ OP= √136

Now by Pythagoras theorem in ∆PBO,

OP² = OB² + BP²

BP² = OP² – OB²

⇒ BP² = (√136) ² – 3²

⇒ BP² = 136 – 9

⇒ BP= √127

Hence, BP= √127 cm