Question

Find the length of tangent drawn to a circle with radius 8 cm form a point 17 cm away from the center of the circle

Answer 1

Let O be the center of the given circle.
Let P be a point, such that
OP = 17 cm.
Let OT be the radius, where
OT = 5cm
Join TP, where TP is a tangent.
Now, tangent drawn from an external point is perpendicular to the radius at the point of contact.

∴ OT ⊥ PT

In the right Δ OTP,we have:

`OP^2 = OT^2 +TP^2 `                [By Pythagoras’ theorem:]

`TP = sqrt(OP^2 - OT^2)`

      `=sqrt(17^2 -8^2)`

      ` =sqrt(289-64)`

     `= sqrt(225)`

      = 15 cm 

∴ The length of the tangent is 15 cm.