Question

Find the length of the tangent drawn from a point whose

distance from the centre of a circle is 5 cm and radius of

the circle is 3 cm.​

Answer 1

Answer:

Hence, length of tangent from P=24 cm.

Step-by-step explanation:

ANSWER

Let P be the given point, O be the centre of the circle and PT be the length 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 point of contact.

∴∠OTP=90o

In right triangle OTP, we have

OP2=OT2+PT2

⇒252=72+PT2

⇒PT2=252−72=(25−7)(25+7)=576

⇒PT=24 cm.

Answer 2

Answer:

Given: PQ is a tangent to the circle intersect at Q. OP = 5 cm and OQ = 3 cm.

To find: PQ

Proof:

In rt.△ OQP, by Pythagoras theorem

Therefore the length of the tangent from a point is 4 cm.