UPSC NDA Math Model Paper 7

Let O be the centre of the circle, P be the point whose is at a distance of 5 cm from the centre.
Suppose the tangent drawn from point P meets the circle at point Q as shown in the figure given below:
In Δ OPQ
⇒ OQ = 3 cm and OP = 5 cm (Given)
As ΔOPQ is right angle at Q.
So, by using pythagoras theorem we get
⇒OQ2+PQ2=OP2
⇒PQ2+32=52
⇒PQ2=25−9=16
⇒PQ=4‌cm
So, the length of the tangent is 4 cm
Hence, option B is the correct answer.