# The length of a t

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,

OA2 = AB2 + OB2

OB2 = OA2 – AB2

OB2 = 102 – 42

OB2 = 100 – 16

OB2 = 84

OB2 = 21 × 2 × 2

OB = 2√21 cm

Therefore the radius of circle OB = 2√21 cm

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