Play with Geometric Shapes in $2$D Coordinate

System

Given two sets of closed geometrical shapes each having a point, a circle, a triangle

and a rectangle, find the following:

Question$-1$: Is the point lie on all closed geometric shapes in set$-1?$

Question$-2$: Is the point lie on all closed geometric shapes in set$-2?$

Question$-3$: Are alike shapes in set$-1$ and set$-2$ intersect?

Question$-4$: Are shapes in set$-1$ bigger than set$-2?$

Note that, all the geometric shapes are filled. This means, if a point is inside a circle

or any other shape, then they are in contact. Similarly, two different radius

concentric circles are also in contact. Just think of filled circle as disk.

Individual display of set$-1$ and set$-2$ geometrical objects in $2$D coordinate

system:

Set$-1$:

Set$-2$:

Display of both sets in one $2$D coordinate plane:

Combined:

Programming hints:

The following classes may required:

point

circle

triangle

rectangle

geometry

Input is two copies a point, circle, triangle, rectangle for set$-1$ and set$-2.$

A point is defined as $P(x,y).$

A circle is defined as radius $r$ and center point $C(x1,y1).$

A triangle is defined as three non collinear points $A(x2,y2),B(x3,y3)$ and $C(x4,y4).$

A rectangle is defined as two points top left $D(x5,y5)$ and bottom right $E(x6,y6).$

Note: Assume that rectangle sides are parallel to coordinate axes.

listing them gives: $x,y,r,x1,y1,x2,y2,x3,y3,x4,y4,x5,y5,x6,y6$

Input Format:

The first line of input will contain a single integer $T,$ denoting the number of test

cases.

Each test case consists of two lines of input, each line contains $15$ values separate

by a space and these two input lines represent the set$-1$ and set$-2$ objects.

Output Format:

For each test case, there are six lines of output which described as$,$

In line$-1$ print true or false.

In line$-2$ print true or false.

In line$-3$ print a boolean array of size $3$ separated by space.

In line$-4$ to $6,$ print a table of size $3$ by $3$ adjacent elements are separated by space.

Constraints:

$-2000x,y-$coordinates $of$ points $2000$

$0$