Draw the two intersecting lines to include an angle of ${{30}^{\circ }}$. You need to Use ruler and compasses to locate points which are at equal distance from these two intersecting lines and also $2cm$ away from their point of intersection. So find How many such points exist?

ATQ,

1. First draw an angle bisector with the help of compass AB and XY of angles formed by the lines e and f.

2. Now, from center draw a circle with the help of compass, of radius $2cm$, which intersect the angle bisector at p, q, r and s respectively.

Therefore, p, q, r and s are the required four points on the circle having radius $2cm$.