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Question

Find the length of the tangent drawn from a point whose distance from the center of a circle is 25 cm. Given that the radius of the circle is 7 cm. [3 MARKS]


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Solution

Concept: 1 Mark
Application: 2 Marks

Let P be the given point , O be the center of the circle and PT be the lenght of tangent from P .

Then, OP= 25 cm and OT = 7 cm

Since tangent to a circle is always perpendicular to the radius through the points of contact.

Therefore , OTP=90

In right triangle OTP , We have

OP2=OT2+PT2

252=72+PT2

PT2=25272=(257)(25+7)=576

PT=24

Hence, length of tangent from P = 24 cm


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