Circles (1) P84786

To solve this exercise you will need the definition of @Point@ and @distance()@ of problem P46254.

Write a procedure

    void move(Point& p1, const Point& p2);

that moves the point @p1@ according to the coordinates indicated by the point @p2@.

For instance, being @p1@ the point $(2, 1)$, and @p2@ the point $(-0.5, 4)$. Then @move(p1, p2)@ would do that @p1@ was $(1.5, 5)$.

Additionally, using the definition

    struct Circle {
        Point center;
        double radius;
    };

write two procedures,

    void scale(Circle& c, double sca);

that scales the circle @c@ proportionately to the real strictly positive @sca@, and

    void move(Circle& c, const Point& p);

that moves the circle @c@ according to the coordinates indicated by @p@.

For instance, being @c@ a circle of center $(1, 2)$ and radius 3. Then, @scale(c, 2)@ would obtain a circle of center $(1, 2)$ and radius 6. However, if @p@ is $(3.5, -1)$, @move(c, p)@ would obtain a circle of center $(4.5, 1)$ and radius 3.

Write also a function that prints if a point @p@ is inside a circle @c@:

    bool is_inside(const Point& p, const Circle& c);

Suppose that the radii are always strictly positive, and that @p@ will never be exactly in the border of @c@.

Observation

You only need to submit the required classes; your main program will be ignored.

Strictly obey the type definitions of the statement.