Question

the length of tangent to circle from a point 17cm from it centre is 8cm find its radius ​

Answer 1

Length of Tangent is 15 cm

Step-by-step explanation:

Let the circle with center O (Radius 8 cm) and P be any point 17 cm away from center O.

Join OP.

Now, With P as center, draw an arc of intersecting the circumference at T(acts as Tangent.)

Now, OP = 17 cm, OT = 8 cm and PT is to be calculated.

We know that, Tangent to a circle is perpendicular to the Radius of circle.

or ΔOTP is Right Angled at T

Hence, we'll follow Pythagoras Theorem:

$OT^2 + PT^2 = OP^2$

or $PT^2 = OP^2 - OT^2$

⇒ $PT^2 = 17^2 - 8^2$

⇒ $PT^2 = 289 - 64$

⇒ $PT^2 = 225$

⇒ $PT = \sqrt 225$

⇒ $PT = 15$

Length of Tangent to Circle from the Point is 17 cm