Draw two intersecting lines to include an angle of 30º. Use ruler and compasses to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such points exist?
Describe completely the locus of points in each of the following cases : (i) mid-point of radii of a circle. (ii) centre of a ball, rolling along a straight line on a level floor. (iii) point in a plane equidistant from a given line.
Construct $\angle \mathrm{ABC}=120^{\circ}$, where $\mathrm{AB}=\mathrm{BC}=5 \mathrm{~cm}$. Mark two points $\mathrm{D}, \mathrm{E}$ which satisfy both the following conditions (a) equidistant from BA and BC (b) at a distance of 5 cm from B . Point E is on the side of reflex $\angle \mathrm{ABC}$. Join $\mathrm{AE}, \mathrm{EC}$, $C D$ and $A D$. Describe the figures (i) $A E C D$ (ii) $A B D$ (iii) $A B E$.
Construct the locus of points inside the triangle ABC, which are equidistant from B and C. Mark the point P which is equidistant from AB, BC and also equidistant from B and C.
Construct a quadrilateral ABCD in which $\mathrm{AB}=5 \mathrm{~cm}, \mathrm{BC}=4 \mathrm{~cm}, \angle \mathrm{~B}=60^{\circ}, \mathrm{AD}=5.5 \mathrm{~cm}$ and D is equidistant from AB and BC .