Odpowiedź:
r - promień okręgu = 41 [j]
d - przekątna trapezu = 80 [j]
[j] - znaczy właściwa jednostka
IAOI = IOBI = r = 41 [j]
IODI = r = 41 [j]
IADI² = IABI² - d² = (2r)² - 80² = (2 * 41)² - 6400 = 82² - 6400 =
= 6724 - 6400 = 324
IADI = √324 = 18 [j]
P - pole trójkąta ABD= √[p(p- a)(p-b)(p - c)] ,gdzie p = (a +b +c)/2
a = IABI= 2r = 2 * 41 = 82 [j]
b = IBDI = 80 [j]
c = IADI= 18[j]
p= (a +b+ c)/2= ( 82+ 80+ 18)/2= 180/2= 90
P = √[p(p-a)(p - b)(p - c)] = √[90(90- 82)(90- 80)(90 - 18)]=
= √(90 * 8 * 10 * 72) = √518400 = 720 [j²]
P = 1/2 * IABI * h
2P = IABI * h
h = 2P : IABI = 2 * 720 : 82 = 1440 : 82 = 17 46/82 = 17 23/41 [j]
x² = r² - h² = 41² - (17 23/41)² = 1681 - (720/41)²=1681 - 518400/1681 =
= (1681 * 1681 - 518400)/1681 = (2825761 - 518400)/1681=
= 2307361/1681
x = √(2307361/168/1) = 1519/41 = 37 2/41 [j]
ICDI = 2x= 2 * 1519/41 = 3038/41 = 74 4/41[j]
O - obwód trapezu = IABI + IADI + ICDI + IBCI = 2 * 41 + 18 + 74 4/41 + 18 =
= 82 + 36 + 74 4/41 = 118+ 74 4/41 = 192 4/41 [j]
Rysunek w załączniku
