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Find the length of the tangent drawn to a circle of radius 3 cm, from a point distant 5 cm from the centre.

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Answer

Let tangent be drawn from point P.

In a circle with centre O and radius = 3 cm and P is at a distance of 5 cm.

Find the length of the tangent drawn to a circle of radius 3 cm, from a point distant 5 cm from the centre. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

OT = 3 cm and OP = 5 cm

OT ⊥ PT

In right angle △OTP,

By pythagoras theorem,

OP2=OT2+PT252=32+PT225=9+PT2PT2=25−9PT2=16PT=16PT=4 cm.OP^2 = OT^2 + PT^2 \\[1em] 5^2 = 3^2 + PT^2 \\[1em] 25 = 9 + PT^2 \\[1em] PT^2 = 25 - 9 \\[1em] PT^2 = 16 \\[1em] PT = \sqrt{16} \\[1em] PT = 4 \text{ cm}.

Hence, the length of tangent = 4 cm.

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