Question

a point p is 25 cm From the centre . the radius of the circle is 7 cm and length of the tangent drawn From p to the circle is x . then find the value of x. ​

Answer 1

Answer:

Step-by-step explanation:

Given- O is the centre of a circle to which a tangent PT=x has been drawn to the circle at T when OP=25cm. The radius of the given circle=7cm

To find out: x=?

Solution- We join OT.

∴OT is a radius of the circle through the point of contact T of the tangent PT. We know that the radius through the point of contact of a tangent to a circle is perpendicular to the tangent.  

∴OT⊥PT⟹∠OTP=90  

∴ΔOTP is a right one with OP as hypotenuse. So, applying Pythagoras theorem, we get

PT=  

OP  ^2

−OT ^2​  

=  

25 ^2

−7^2  

cm=24cm^2.

∴ The tangent to the given circle PT=24cm