Answer :

Given:

Distance of point from center, OA = 10 cm

Length of tangent, AB = 4 cm.

Solution:

The diagram for the question is as follows:

Let the centre be O.

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

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

OB ⊥ AB

Hence Δ OAB is right angled triangle.

∠ OBA = 90°

By Pythagoras theorem,

OA^{2} = AB^{2} + OB^{2}

OB^{2} = OA^{2} – AB^{2}

OB^{2} = 10^{2} – 4^{2}

OB^{2} = 100 – 16

OB^{2} = 84

OB^{2} = 21 × 2 × 2

OB = 2√21 cm

Therefore the radius of circle OB = 2√21 cm

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