Write a program that prompts the user to enter points using the
keyboard. In all tasks you have a coordinate system on the plane and
all points
are defined with their coordinates in this coordinate system. Triangles
are defined by their vertexes; circles
are
defined by their centers (which are points) and their radius (which
are numbers). Make the calculations and print out the results. Your
program must be tested with an example given after every task. Also it
can work with arbitrary input data.

The number of your particular task
is the value of the
expression
`faculty_number%25`
(remainder of integer division; f
mod 25).

Model task: Enter a triangle and calculate the length of its minimal
side.

Example: (2, 3); (5, 2.5); (1, -1)

Solution

0. Enter a triangle and calculate its area. Print out "too small"
when the area is less than 1.

http://en.wikipedia.org/wiki/Triangle

Example: (2, 3); (5, 2.5); (1, -1)

1. Enter a convex quadrilateral with vertexes in different quadrants
and calculate its area. Print out "too small" when the area is less
than 1.

http://en.wikipedia.org/wiki/Quadrilateral

Example: (2, 3); (-5, 2.5); (-1,-1); (2, 3.5)

2. Enter a triangle and calculate its perimeter. Print out "too
small" when the perimeter is less than 1.

http://en.wikipedia.org/wiki/Triangle

Example: (-2,3); (5,4); (1,0)

3. Enter a triangle and calculate the radius of its circumscribed
circle. Print out "too small" when the radius is less than 1.

http://en.wikipedia.org/wiki/Circumscribed

Example: (2,2.1); (-3,2.5); (0,0)

4. Enter a triangle and calculate the radius of its inscribed circle.
Print out "too small" when the radius is less than 1.

http://en.wikipedia.org/wiki/Inscribed

Example: (2,2.1); (-3,2.5); (0,0)

5. Enter a triangle and determine its type -
acute-angled, obtuse-angled or right-angled.

http://en.wikipedia.org/wiki/Angle#Types_of_angles

Example: (0,0); (25,0); (0,50)

6. Enter a triangle and calculate the bisector length of its
maximal angle.

http://en.wikipedia.org/wiki/Angle_bisector#Angle_bisector

Example: (3,1); (-1,2.5); (0,0.5)

7. Enter a triangle and calculate the sine of its
maximal angle.

http://en.wikipedia.org/wiki/Sine

Example: (-2.0,4.0); (-3.0,2.5); (0.0,2.0)

8. Enter a triangle and calculate the cosine of its
minimal angle.

http://en.wikipedia.org/wiki/Sine

Example: (-2.0,4.0); (-3.0,2.5); (0.0,2.0)

9. Enter a triangle and
calculate its the minimal altitude.

http://en.wikipedia.org/wiki/Triangle

Example: (3,1); (-1,2.5); (0,0.5)

10. Enter a triangle and
its minimal median.

http://en.wikipedia.org/wiki/Triangle

Example: (31,30); (-10,1); (0,55)

11. Enter a triangle and calculate the ratio
of its maximal and minimal sides.

http://en.wikipedia.org/wiki/Triangle

Example: (35,0); (-12,5); (0,0)

12. Enter four points and choose three of them which are vertexes of
the triangle with the smallest area.

http://en.wikipedia.org/wiki/Area

Example: (3,1); (0,0); (2,2); (-1,0)

13. Enter a triangle and find a point placed inside it.

http://en.wikipedia.org/wiki/Triangle

Example: (3,4); (-3,2.5); (0,-4.2)

14. Enter a triangle and calculate the distance between its
mass center (center of gravity) and the origin of the coordinate
system.

http://en.wikipedia.org/wiki/Triangle

Example: (3,0); (-1.5,2.5); (0,0)

15. Enter four points and find two of them with the maximal
distance.

http://en.wikipedia.org/wiki/Distance

Example: (30,10); (-10,0); (20,20); (-10,0)

16. Enter four points and calculate the length of the sum of segment
lines,
connecting these points successively.

http://en.wikipedia.org/wiki/Distance

Example: (0,0), (0.12, 0.01), (-0.19,0); (0.10,0.15)

17. Enter four points and calculate the sum lengths of all segment
lines,
connecting the points.

http://en.wikipedia.org/wiki/Distance

Example: (0,0), (0.12, 0.01), (-0.19,0); (0.10,0.15)

18. Enter a segment line and check whether it intersects the
coordinate axes.

http://en.wikipedia.org/wiki/Coordinate_axes

Example: (-3,4), (4,1)

19. Enter a circle and a segment line. Check whether the line lies
into the circle.

http://en.wikipedia.org/wiki/Line_segment

Example: (0.022,0.023), 0.1; (-0.01,0), (0,0)

20. Enter a circle and a segment line. Check whether the circle
intersects the line at only one point.

http://en.wikipedia.org/wiki/Line_segment

Example: (0.022,0.023), 0.1; (-0.01,0), (0,0)

21. Enter a circle and a point. Check whether the point lies into
the circle.

http://en.wikipedia.org/wiki/Circle

Example: (0.2,0.2), 1; (-0.1,0)

22. Enter a circle and a triangle. Check whether the triangle lies
into the circle.

http://en.wikipedia.org/wiki/Circle

Example: (0.2,0.2), 1; (-0.1,0); (0.01, 0.1); (0.1, -0.1)

23. Enter five points and find a circle containing all these points.

http://en.wikipedia.org/wiki/Circle

Example: (3,1); (-1,0); (-2,2); (-1,2); (1,-1)

24. Enter two circles and determine whether they intersect or not.

http://en.wikipedia.org/wiki/Circle

Example: (-2,4), 5; (-3,2), 6