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.PS
# Geometry.m4
gen_init
Fig1: [ ls = 2/3 # local scale
A: Here; "A" at A above
B: A+(-1*ls,-3.5*ls); "B" at B below rjust
C: B+(4.6*ls,0); "C" at C below ljust
AB: line from A to B
BC: line from B to C
CA: line from C to A
PerpTo(A,BC,L); "L" at L below
AL: line from A to L; RightAngle(A,L,C)
angleLAC = atan2(C.x-L.x,A.y-L.y)
S: move from A to (sin(angleLAC/2),-cos(angleLAC/2))
AW: line from A to Intersect_(S,BC)
W: Here; "W" at W below rjust
PerpTo(C,AB,N); "N" at N above rjust
CN: line from C to N; RightAngle(C,N,B)
PerpTo(B,CA,M); "M" at M above
CM: line from B to M; RightAngle(B,M,C)
H: Intersect_(CN,AL); "H" at H +(4bp__,10bp__)
thinlines_
Equidist3(B,L,N,CC1,c1rad); C1: circle rad c1rad at CC1
Equidist3(B,W,N,CC2,c2rad); C2: circle rad c2rad at CC2
Equidist3(B,C,N,CC3,c3rad); C3: circle rad c3rad at CC3
Equidist3(W,C,M,CC4,c4rad); C4: circle rad c4rad at CC4
thicklines_
Z: LCintersect(AW,CC2,C2.rad); "Z" at Z+(-5bp__,-5bp__)
HZ: move from H to Z
Y: LCintersect(HZ,CC4,C4.rad,R); "Y" at Y above
X: LCintersect(HZ,CC2,C2.rad); "X" at X above rjust
Loopover_(`P',`dot(at P)',X,Y,Z)
line dashed from X to Y chop -linewid/2
RightAngle(A,Z,Y)
]
Fig2: [ ls = 3/4 # local scale
# https://tex.stackexchange.com/questions/593272/drawing-complex-geometry
P: dot(at Here); "P" at P.s below
N: dot(at P+(3.5*ls,1.5*ls)); "N" at N.se ljust below
O: dot(at (N,P)); "O" at O.s below
R: dot(at 1/3 between O and P);"R" at R.s below
M: dot(at (R,N)); "M" at M.se ljust below
Q: dot(at (M.x,M.y+distance(M,N)/distance(N,O)*distance(P,O)));"Q" at Q.e ljust
line from P to Q then to N then to O
B: line to P chop -0.3
line from M to N
Pu: line from R to Q chop 0 chop -0.3
H: line from P to N chop 0 chop -0.3
X: dot(at Intersect_(Pu,H)); "X" at X.se ljust below
thinlines_
RightAngle(Q,M,N)
RightAngle(Q,N,H.end)
RightAngle(N,O,B.start)
ArcAngle(N,P,Q,0.4); "$\beta$" at last arc.ne above ljust
ArcAngle(O,P,N,0.5); "$\alpha$" at last arc.start+(5bp__,8bp__)
ArcAngle(R,Q,N,0.5); "$\alpha$" at last arc.start+(8bp__,-5bp__)
] with .w at Fig1.e+(-0.4,0)
.PE
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