A particle has two velocities of equal magnitude inclined to each other at an angle $\theta$. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. The $\theta$ is :

Question

( A ) $90^{\circ}$
( B ) $60^{\circ}$
( C ) $120^{\circ}$
( D ) $45^{\circ}$