Coordinate Geometry

Let $$P\left(x,y\right)$$ be the Cartesian  coordinates with respect to axes $$OX$$ and $$OY$$ then $$\left(r,\theta\right)$$ be its polar coordinates with respect to pole $$O$$ and initial line $$OX$$ i.e.$$OP=r$$(radius vector) and $$\angle{XOP}=\theta$$ (vectorial angle)
Now, let $$p$$ be the length of the perpendicular from $$O$$ upon straight line(through $$A,B$$)
i.e.,$$OM=p$$ and $$\angle{XOM}=\alpha$$

Rita goes $$20\ km$$ towards East from a point $$A$$ to the point $$B$$. From $$B$$, she moves $$30km$$ towards west along the same road. If the distance towards east is represented by a positive integer then, how will you represent the distance travelled towards West?
A locus is a curve traced out by a point which moves under certain geometrical conditions:To find the locus of a point first we assume the coordinates of the moving point as $$(h,k)$$ and then try to find a relation between $$h$$ and $$k$$ with the help of the given conditions of the problem. If there is any variable involved in the process then we eliminate them. At last, we replace $$h$$ by $$x$$ and $$k$$ by $$y$$ and get the locus of the point which will be an equation in $$x$$ and $$y$$.
$$ABCD$$ is a quadrilateral. A circle is inscribed touching all four sides of the quadrilateral at $$P, Q, R, S$$ respectively.
On the basis of above passage answer the following questions,
Draw the figure according to the given information and answer the questions.