1a. OABC et H

Angles en O

Angles en H

1.b : (AH)⊥(BC)

(BH)⊥(AC)

1c. Position de H dans ABC

2a . Afficher le repère

3a. Distance de O à (ABC)

3b. Aire ABC=

+

+

=

3c. Somme des aires

tt = 0.15
α = 0.8726646259971648 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
β = 0.3839724354387525 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
O = (5.84, -1.5)
u, v, w = ThreeDReferential(O, α, β)
C: O + 3 w
Zc: Vector[O, C] w / Length[w]^(2)
B: O + 2 v
Yb: Vector[O, B] v / Length[v]^(2)
A: O + u
Xa: Vector[O, A] u / Length[u]^(2)
CH: A + Xa^(2) / (Xa^(2) + Yb^(2)) Vector[A, B]
l = Line(C, CH)
BH: A + Xa^(2) / (Xa^(2) + Zc^(2)) Vector[A, C]
k = Line(B, BH)
H = Intersect(k, l)
HH2: H + tt Vector[H, C] / Length[Vector[H, C]]
HH1: H + tt Vector[H, O] / Length[Vector[H, O]]
HH3 = Midpoint(HH1, HH2)
HH4 = Mirror(H, HH3)
t = Segment(HH2, HH4)
poly1, b', c', o = Polygon(C, O, B)
poly2, o_1, c'_1, a' = Polygon(C, A, O)
poly3, a'_1, b'_1, o_2 = Polygon(B, O, A)
poly4, a'_2, c'_2, b'_2 = Polygon(C, B, A)
d = true
B1: O + t v
C1: O + t w
A1: O + tt u
AB1: A1 + tt v
AC1: A1 + tt w
BC1: B1 + t w
e = Segment(A1, AB1)
f = Segment(B1, AB1)
g = Segment(C1, AC1)
h = Segment(A1, AC1)
i = Segment(B1, BC1)
j = Segment(C1, BC1)
m = Segment(O, H)
BH1: BH + t Vector[BH, B] / Length[Vector[BH, B]]
BH2: BH + t Vector[BH, C] / Length[Vector[BH, C]]
BH3 = Midpoint(BH1, BH2)
BH4 = Mirror(BH, BH3)
n = Segment(BH2, BH4)
p = Segment(BH1, BH4)
CH1: CH + t Vector[CH, C] / Length[Vector[CH, C]]
CH2: CH + t Vector[CH, B] / Length[Vector[CH, B]]
CH3 = Midpoint(CH1, CH2)
CH4 = Mirror(CH, CH3)
q = Segment(CH2, CH4)
r = Segment(CH1, CH4)
s = Segment(HH1, HH4)
b_1 = Segment(C, CH)
HH5: H + tt Vector[H, B] / Length[Vector[H, B]]
HH6 = Midpoint(HH1, HH5)
HH7 = Mirror(H, HH6)
a_1 = Segment(HH5, HH7)
c_1 = Segment(HH1, HH7)
d_1 = Segment(B, BH)
z = false
e_1 = false
f_1 = Line(A, H)
AH = Intersect(f_1, a'_2)
AH1: AH + tt Vector[AH, A] / Length[Vector[AH, A]]
AH2: AH + tt Vector[AH, B] / Length[Vector[AH, B]]
AH3 = Midpoint(AH1, AH2)
AH4 = Mirror(AH, AH3)
g_1 = Segment(AH1, AH4)
h_1 = Segment(AH2, AH4)
i_1 = false
j_1 = false
k_1 = false
a = false
text1: m + ""
b = false
D = Midpoint(O, H)
text2: poly4 + ""
c = false
text3: "" + poly1 + "²"
text4: "" + poly2 + "²"
text5: "" + poly3 + "²"
text9: "" + poly4 + "²"
l_1 = false

Tool: ThreeDReferential
Input: A, th, phi
Output: i, j, k

i = Vector(A, A - sin(th) Vector[(1, 0)] - sin(phi) cos(th) Vector[(0, 1)])
j = Vector(A, A + cos(th) Vector[(1, 0)] - sin(phi) sin(th) Vector[(0, 1)])
k = Vector(A, A + cos(phi) Vector[(0, 1)])