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A point P is at a distance of 29 cm from the centre of a circle of radius 20 cm. Find the length of the tangent drawn from P to the circle.

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Let O be the center of circle, OP = 29 cm (given)

Radius of a circle = 20 cm

Let T be any point on the circumference of the circle, then PT is the tangent to the circle.

From Figure:

OT is radius and PT is the tangent

This implies, OT ⊥ PT

In right ∆OPT,

By Pythagoras Theorem:

OP2 = OT2 + PT2

(29)2 = (20)2 + PT2

841 = 400 + PT2

PT2 = 441

or PT = 21

Length of tangent PT is 21 cm

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