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]
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=252−72=(25−7)(25+7)=576
⇒PT=24
Hence, length of tangent from P = 24 cm