Question

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

Answer 1

Step-by-step explanation:

P is any point outside the circle

and the distance between P and the point of tangency (point Q) on the circumference of the circle is 15cm

And, the distance from the center of the circle (point O) to point P is given 17cm

therefore we can say triangle OPQ is right angled triangle (at Q)

[tangent is perpendicular to radius]

Hence,

PQ=15cm

OP=17cm

OQ= x cm

=> (OP)^2 = (PQ)^2 +(OQ)^2

=> 17^2 - 15^2 = (x)^2

=> x = {289 - 225}^1/2 [sq.rt.]

=> x = {64}^1/2

=> x = 8 cm

Thus, OQ is equal to 8cm

Therefore the radius of the circle is equal to 8cm

Hope this helps you :)