Răspuns:
1.
a) AC= 12 cm
b)
[tex]AB= \: 3 \sqrt{5} [/tex]
2. DB= 7 cm
3.
[tex]AB =\:18 \sqrt{3} cm[/tex]
Explicație:
1.
a)
[tex] {AC}^{2} = CD \times CB[/tex]
[tex]{AC}^{2} = 6 \times 24 \\ {AC}^{2} = 144 \\ AC = \sqrt{144} = 12 \: cm[/tex]
b)
[tex] {AB}^{2} = BD \times BC \\ {AB}^{2} = 3 \times 15 \\ AB = \sqrt{45} = 3 \sqrt{5} cm[/tex]
2.
CB = CD + DB
[tex] {AC}^{2} = DC \: \times BC \\ {AC}^{2} = DC \: \times (DC +BD) \\ {12}^{2} = 16 \times (16 +BD) \\ 144 = 256 + 16BD \\ 256 - 144 = 16BD \\ 112 = 16BD \\ BD = 112 \div 16 = 7cm[/tex]
3.
ABC: m(A)=90° =>
[tex] {AB}^{2} = {BC}^{2} - {AC}^{2} \\ {AB}^{2} = {36}^{2} - {18}^{2} \\ {AB}^{2} = 1296 - 324 \\ AB = \sqrt{972} = 18 \sqrt{3} cm[/tex]
