% Sheila Shah
% MAKE CONSTRUCTION




%!




% takes in 2 points in vector form and finds the midpoint
/findmidpoint { 10 dict begin

	/B exch def
	/A exch def

	[A 0 get B 0 get add 2 div A 1 get B 1 get add 2 div]

end} def


%takes in stack of 3 2D vectors, 3 points
/mktriangle { 16 dict begin

	/C exch def
	/B exch def
	/A exch def

	A 0 get A 1 get moveto
	B 0 get B 1 get lineto
	C 0 get C 1 get lineto
	closepath

end } def


% takes in x, y, and size

/mkcircle {16 dict begin

/size exch def
/y exch def
/x exch def
/N 64 def


/a 0 def
a cos size mul x add a sin size mul y add moveto
N {
/a a 360 N div add def
a cos size mul x add a sin size mul y add lineto
} repeat

end } def



%takes in a stack of 3 2D vectors, 3 points
% and makes an inscribed circle in the triangle outputs centre[x y]

/mkinscribedcircle { 20 dict begin

	/C exch def
	/B exch def
	/A exch def



	/aa [B 0 get C 0 get sub B 1 get C 1 get sub] def
	/bb [C 0 get A 0 get sub C 1 get A 1 get sub] def
	/cc [B 0 get A 0 get sub B 1 get A 1 get sub] def

	/a aa 0 get 2 exp aa 1 get 2 exp add 0.5 exp def
	/b bb 0 get 2 exp bb 1 get 2 exp add 0.5 exp def
	/c cc 0 get 2 exp cc 1 get 2 exp add 0.5 exp def

	/s a b add c add 2 div def
	/k s a sub s b sub mul s c sub mul s mul 0.5 exp def

	/r k s div def

	%finding the centre of the circle

	/sinA B 1 get A 1 get sub c div def
	/angle sinA dup 2 exp 1 sub neg sqrt atan def

	/d 1 angle 2 div sin angle 2 div cos div div r mul def



	[A 0 get d add A 1 get r add]

end} def


% takes in 3 vector, points and outputs a vector [xcentre, ycentre,R radius]
/mkcircumcircle { 20 dict begin

	/C exch def
	/B exch def
	/A exch def



	/aa [B 0 get C 0 get sub B 1 get C 1 get sub] def
	/bb [C 0 get A 0 get sub C 1 get A 1 get sub] def
	/cc [B 0 get A 0 get sub B 1 get A 1 get sub] def

	/a aa 0 get 2 exp aa 1 get 2 exp add 0.5 exp def
	/b bb 0 get 2 exp bb 1 get 2 exp add 0.5 exp def
	/c cc 0 get 2 exp cc 1 get 2 exp add 0.5 exp def


	/k 0.5 b mul B 1 get A 1 get sub mul def

	/R a b mul c mul 4 k mul div def

	% coordinates of circumcircle

	/x A 0 get b 2 div add  def
	/y R 2 exp b 2 div 2 exp sub 0.5 exp A 1 get add def

	[x y R]

end} def


/Times-Roman findfont
0.1 scalefont
setfont

/point 0.03 def




%--------------------PAGE 1
gsave
100 dup scale
2 5.5 translate
1 72 div setlinewidth


/A [0 0] def
/B [0.5 1.375] def
/C [1 0] def

A B C mktriangle stroke

0 0 1 setrgbcolor
A 0 get A 1 get point  mkcircle fill
B 0 get B 1 get point mkcircle fill
C 0 get C 1 get point mkcircle fill

-0.33 0 moveto
( A(0,0) ) show
0.3 1.43 moveto
( B(0.5, 1.375) ) show
1.01 0 moveto
( C(1, 0) ) show
showpage
grestore