### Coordinate Geometry

goals
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.