Answer :

Let the diagram be as follows:

P divides the line AB in the ratio 3:1

Adding 1 both side, we get

⇒ BP = 2 cm

And hence,

AP = 3BP = 3(2) = 6 cm

Let the centre be O.

From this figure it can be interpreted that OP will be the radius of the circle.

Radius OP is perpendicular to the tangent AB as radius is perpendicular to the tangent.

If OP is ⊥ to AB which implies that OP is ⊥ AP and OP is ⊥ PB.

Hence Δ OPA is right angled triangle

∠ OPA = 90°

OA^{2} = AP^{2} + OP^{2}

OP^{2} = OA^{2} – AP^{2}

OP^{2} = 10^{2} – 6^{2}

OP^{2} = 100 – 36

OP^{2} = 64

∴ OP = 8 cm

Therefore the radius of circle = 8 cm.

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