Question

From a point P ,the lenght of the tangent to a circle is 15 cm and distance of P from the center of the circle is 17 cm. Then what is the radius of the circle ​

Answer 1

Answer:

Let the centre of circle be O

so that PO = 17 cm

Tangent is PB whose length is 15 cm

OB is radius as shown

Now we know that radius is perpendicular to point of contact

Hence OB is perpendicular to PB

Hence ∠PBO = 90°

Consider ΔPBO Using Pythagoras theorem ⇒ PB2 + OB2 = PO2

⇒ 152 + OB2 = 172

⇒ OB2 = 172 - 152

⇒ OB2 = 289 – 225 ⇒ OB2 = 64

⇒ OB = ±8

As length cannot be negative ⇒ OB = 8 cm

Hence length of radius is 8 cm

Answer 2

Answer:

8 cm

Step-by-step explanation:

Let centre be O

And tangent's point be R

Then,by Pythagorean theorem,as OPR is right angle triangle.

And OR is the radius of circle.

(OP)²= (OR)² + (RP)²

(17)² = (OR)² + (15)²

289 = (OR)²+ 225

(OR)² = 289 - 225

OR = √64

OR = 8 cm