Jahr 2013 Berechnung

Berechnung

a = Kathete a
b = Kathete b
c = Hypotenuse
r_i = Inkreisradius
r_a = Ankreisradius_a (Kathetenankreisradius a)
r_b = Ankreisradius_b (Kathetenankreisradius b)
r_c = Ankreisradius_c (Hypotenusenankreisradius)

a = √(c²-b²)
r_c = (a+b+c)/2
r_i = r_c-c
r_a = a-r_i
r_b = b-r_i

F₁ = a*b/2
F₂ = a*r_a/2
F₃ = b*r_b/2
F₄ = c*r_c/2
F₅ = (r_c-b)*r_c/2
F₆ = (r_c-a)*r_c/2
F₇ = r_c*r_b/2-F₃
F₈ = r_c*r_a/2-F₂

Vorgaben:
b = 11
c = 61

Ergebnisse:
a = √(61²-11²) = 60
r_c = (60+11+61)/2 = 66
r_i = 66-61 = 5
r_a = 60-5 = 55
r_b = 11-5 = 6

F₁ = 60*11/2 = 330
F₂ = 60*55/2 = 1650
F₃ = 11*6/2 = 33
F₄ = 61*66/2 = 2013
F₅ = (66-11)*66/2 = 1815
F₆ = (66-60)*66/2 = 198
F₇ = 66*6/2-33 = 165
F₈ = 66*55/2-1650 = 165

F1+F2+F3 = 2013
F4 = 2013
F5+F6 = 2013

F2+F3+F7+F8 = 2013
F4 = 2013
F5+F6 = 2013

F2+F6+F8 = 2013
F3+F5+F7 = 2013
F4 = 2013