N is the foot of the perpendicular from a point P of a circle with radius 7 cm, on a diameter AB of the circle. If the length of the chord PB is 12 cm, the distance of the point N from the point B is

As we know $$cos\theta$$ = $$\frac{a^2 + b^2 - c^2}{2ab}$$ (where $$\theta$$ is angle between sides a and b, side c is opposite to angle $$\theta$$ )
Hence for triangle POB (where O is centre of circle)
OP=OB=radius of circle=7
PB=12
Let's say angle between PB and OB is $$\theta$$.
So putting up values and solving it, we will get $$cos\theta$$ = $$\frac{6}{7}$$
Hence value of BN will be BP $$cos\theta = 12cos\theta = \frac{72}{7}$$