Question

A tangent is drawn to a circle of a radius 3cm from an external point of distance 5cm away from the centre find the length of the tangent

Answer 1

Answer:

4cm

Step-by-step explanation:

Radius = 3cm

distance from centre to the point = 5cm

we know that tangent is perpendicular to the radius

therefore,

        length of tangent = square root of 5^2-3^2

                                     = square root of 25-9

                                      = square root of 16

                                     = 4cm

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Answer 2

Step-by-step explanation:

In ∆OPA,

Angle OPA = 90° (The tangent of a circle is perpendicular to the radius through the point of contact.)

By Pythagoras theorem,

${ OA}^{2} = {OP}^{2} + {PA}^{2}$

${5}^{2} = {3}^{2} + {PA}^{2}$

$25 = 9 + {PA}^{2}$

$25 - 9 = {PA}^{2}$

$16 = {PA}^{2}$

$PA = \sqrt{16}$

$PA = 4cm$