Angle \;de\; tir \;maximal

V

V'

\mathscr{C}

A

B

H

M

I

d

Angle\;de\;tir\;maximal

Conjectures:\
b) d'après\;la\;courbe\;décrite\;par\;V:\
*\;la\;valeur\;maximale\;de\;\alpha\;est

Conjectures\;d'après\;les\;traces\;des\;points:\
b)\;celles\;de\;V:\;la\;valeur \;maximale\;prise\;par\
\alpha\;est\;8°.474\;elle\;est\;atteinte\;quand\;x≈18.8m\
c)\;celles\;de\;I:centre \;de\; \mathscr{C}\;est\; une\;demi-\
droite\;\left( ou\;un\;segment  \right) \;parallèle\;à\;d      \
d)\;celles\;de\;V':\;lorsque\;\alpha\;atteint\;son\;maximum\
\widehat{IMH}\;est\;droit\;par\;suite\;d\;est\;tangente\;à\;\mathscr{C}

Conjectures\;d'après\;le\;tableur\;(ligne\;70):\
b)\;la\;valeur \;maximale\;prise\;par\;y(V)=\alpha\;est\
8°.4745\;elle\;est\;atteinte\;quand\;x=x(V)=18.8m\
d)\;lorsque\;\alpha=y(V)\;atteint\;son\;maximum\
\widehat{IMH}=89.9775°:\;il\;est\;droit\;par\;suite\
d\;est\;tangente\;à\;\mathscr{C}

β

H = (0, 0)
m = 25 (slider from 0 to 25, step 0.1)
M: (m, 0)
A = (0, 21.8)
B = (0, 16.2)
N = (-2, 0)
a = Ray(N, H)
N' = (0, -2)
b = Ray(N', H)
ζ = Circle(B, A, M)
d = Segment(B, M)
e = Segment(A, M)
I = Center(ζ)
α = Angle(A, M, B)
f = Segment(I, M)
β = Angle(I, M, H)
V: (m, α * 180 / π)
V': (m, β)
g = OrthogonalLine(V', xAxis)
C = Intersect(g, xAxis)
h = OrthogonalLine(V', yAxis)
D = Intersect(h, yAxis)
i = OrthogonalLine(V, yAxis)
E = Intersect(i, yAxis)
texte4: "\widehat{IMH}=" + (LaTeX[β]) + ""
texte3: "\widehat{AMB=}\alpha=" + (LaTeX[α]) + ""
j = Segment(V', D)
k = Segment(V, E)
l = Segment(V, C)
F = Point(ζ)
texte13: "x=" + (LaTeX[m]) + ""
texte5: "x=" + (LaTeX[m]) + ""
G = Point(a)
texte18: "Curseur\; de\; commande \;de\; x=" + (LaTeX[m]) + "\\
Animer\;x\;et\; noter\;les\;lignes\; décrites\; par :\\
*\; I :\;dans\; la\; partie\; Graphique\;\left( à\;gauche  \right)\\
*\;V\;et\;V':\; dans \;la\; partie \;Graphique\; 2\;\; \left(  à\;droite \right) "
texte17: "\;\;\;\;\;\;\;\;\;V\left(x=" + (LaTeX[m]) + "  \;\;,\alpha=" + (LaTeX[α]) + " \right) \\
V'\left(  x=" + (LaTeX[m]) + "\;\;,\widehat{IMH} =\beta=" + (LaTeX[β]) + "\right) "
A1: "x(" + (Name[V] + ")")
B1: "y(" + (Name[V] + ")")
C204 = 2.1502425690405786 rad
A2 = 5.20000000000001
B2 = 4.37980544208948
C2 = 2.5968374784089696 rad
A3 = 5.40000000000001
B3 = 4.522454146402
C3 = 2.577023259921694 rad
A4 = 5.60000000000001
B4 = 4.66250838091127
C4 = 2.5573283503850264 rad
A5 = 5.80000000000001
B5 = 4.79992594017998
C5 = 2.537755562917514 rad
A6 = 6
B6 = 4.93466899690397
C6 = 2.5183075710599714 rad
A7 = 6.20000000000001
B7 = 5.0667040447657
C7 = 2.498986909011273 rad
A8 = 6.40000000000001
B8 = 5.19600182969142
C8 = 2.4797959721828113 rad
A9 = 6.60000000000001
B9 = 5.32253727035504
C9 = 2.460737018055542 rad
A10 = 6.80000000000001
B10 = 5.44628936879125
C10 = 2.4418121673224187 rad
A11 = 7
B11 = 5.5672411119912
C11 = 2.423023405298609 rad
A12 = 7.20000000000001
B12 = 5.68537936535807
C12 = 2.404372583581784 rad
A13 = 7.40000000000001
B13 = 5.80069475889632
C13 = 2.385861421944166 rad
A14 = 7.60000000000001
B14 = 5.91318156699945
C14 = 2.3674915104384033 rad
A15 = 7.80000000000001
B15 = 6.02283758268541
C15 = 2.34926431169907 rad
A16 = 8
B16 = 6.1296639871083
C16 = 2.3311811634218316 rad
A17 = 8.20000000000001
B17 = 6.23366521515024
C17 = 2.3132432810027552 rad
A18 = 8.40000000000001
B18 = 6.33484881786786
C18 = 2.295451760320342 rad
A19 = 8.60000000000001
B19 = 6.43322532253525
C19 = 2.2778075806436666 rad
A20 = 8.80000000000001
B20 = 6.52880809099012
C20 = 2.2603116076499643 rad
A21 = 9
B21 = 6.62161317695177
C21 = 2.2429645965363787 rad
A22 = 9.20000000000001
B22 = 6.71165918294029
C22 = 2.225767195210352 rad
A23 = 9.40000000000001
B23 = 6.79896711738535
C23 = 2.2087199475446146 rad
A24 = 9.60000000000001
B24 = 6.88356025247131
C24 = 2.191823296682644 rad
A25 = 9.80000000000001
B25 = 6.9654639832235
C25 = 2.175077588382037 rad
A26 = 10
B26 = 7.04470568829827
C26 = 2.1584830743832892 rad
A27 = 10.2
B27 = 7.12131459289758
C27 = 2.1420399157925436 rad
A28 = 10.4
B28 = 7.19532163418816
C28 = 2.1257481864676313 rad
A29 = 10.6
B29 = 7.26675932956459
C29 = 2.109607876397483 rad
A30 = 10.8
B30 = 7.3356616480572
C30 = 2.093618895065536 rad
A31 = 11
B31 = 7.40206388514738
C31 = 2.0777810747889345 rad
A32 = 11.2
B32 = 7.46600254121755
C32 = 2.062094174025471 rad
A33 = 11.4
B33 = 7.52751520382769
C33 = 2.0465578806414926 rad
A34 = 11.6
B34 = 7.58664043397855
C34 = 2.0311718151341243 rad
A35 = 11.8
B35 = 7.64341765649001
C35 = 2.0159355338023612 rad
A36 = 12
B36 = 7.69788705459482
C36 = 2.000848531861745 rad
A37 = 12.2
B37 = 7.75008946882037
C37 = 1.9859102464981855 rad
A38 = 12.4
B38 = 7.80006630020671
C38 = 1.9711200598570995 rad
A39 = 12.6
B39 = 7.84785941788515
C39 = 1.9564773019641655 rad
A40 = 12.8
B40 = 7.89351107102144
C40 = 1.9419812535752372 rad
A41 = 13
B41 = 7.93706380510753
C41 = 1.9276311489526574 rad
A42 = 13.2
B42 = 7.97856038256859
C42 = 1.9134261785660485 rad
A43 = 13.4
B43 = 8.01804370763651
C43 = 1.8993654917163296 rad
A44 = 13.6
B44 = 8.0555567554265
C44 = 1.88544819908126 rad
A45 = 13.8
B45 = 8.09114250514152
C45 = 1.8716733751821488 rad
A46 = 14
B46 = 8.12484387731795
C46 = 1.8580400607710996 rad
A47 = 14.2
B47 = 8.15670367501661
C47 = 1.8445472651383865 rad
A48 = 14.4
B48 = 8.18676452885528
C48 = 1.831193968340351 rad
A49 = 14.6
B49 = 8.21506884577171
C49 = 1.8179791233479703 rad
A50 = 14.8
B50 = 8.24165876140092
C50 = 1.8049016581166801 rad
A51 = 15
B51 = 8.26657609594563
C51 = 1.7919604775781781 rad
A52 = 15.2
B52 = 8.28986231341563
C52 = 1.7791544655552252 rad
A53 = 15.4
B53 = 8.31155848410884
C53 = 1.7664824866003666 rad
A54 = 15.6
B54 = 8.33170525020549
C54 = 1.7539433877600243 rad
A55 = 15.8
B55 = 8.35034279434579
C55 = 1.7415360002651428 rad
A56 = 16
B56 = 8.36751081106113
C56 = 1.7292591411498726 rad
A57 = 16.2
B57 = 8.38324848092937
C57 = 1.7171116147999328 rad
A58 = 16.4
B58 = 8.39759444732577
C58 = 1.705092214432179 rad
A59 = 16.6
B59 = 8.41058679564237
C59 = 1.6931997235071166 rad
A60 = 16.8
B60 = 8.42226303485082
C60 = 1.6814329170761027 rad
A61 = 17
B61 = 8.43266008128566
C61 = 1.6697905630649856 rad
A62 = 17.2
B62 = 8.44181424452789
C62 = 1.6582714234960547 rad
A63 = 17.4
B63 = 8.44976121527139
C63 = 1.6468742556500564 rad
A64 = 17.6
B64 = 8.45653605505799
C64 = 1.6355978131702071 rad
A65 = 17.8
B65 = 8.46217318777026
C65 = 1.6244408471099856 rad
A66 = 18
B66 = 8.46670639277462
C66 = 1.613402106926587 rad
A67 = 18.2
B67 = 8.47016879961083
C67 = 1.602480341421899 rad
A68 = 18.4
B68 = 8.47259288412795
C68 = 1.5916742996327697 rad
A69 = 18.6
B69 = 8.47401046597012
C69 = 1.5809827316724503 rad
A70 = 18.8
B70 = 8.47445270731977
C70 = 1.5704043895249382 rad
A71 = 19
B71 = 8.47395011280941
C71 = 1.5599380277940242 rad
A72 = 19.2
B72 = 8.47253253051712
C72 = 1.5495824044087552 rad
A73 = 19.4
B73 = 8.47022915396431
C73 = 1.5393362812870188 rad
A74 = 19.6
B74 = 8.46706852503872
C74 = 1.5291984249589088 rad
A75 = 19.8
B75 = 8.46307853776835
C75 = 1.5191676071515015 rad
A76 = 20
B76 = 8.45828644287675
C76 = 1.5092426053366583 rad