РЕШЕНИЕ:
a =9 и b =12
∆BCD ∞ ∆ CAD
BC =
BD
AC
_ CD
12x =
9 + 12 + y
9x
_ CD
12 CD = 9 (21 + y)
4 CD = 3 (21 + y)
4 CD = 63 + 3y
y = 4 CD / 3 – 21
CD
2 = AD ∙ BD
CD2 = y ∙ (9 + 12 + y)
CD
2 = (4 CD / 3 – 21) ∙ (9 + 12 + 4 CD / 3 – 21)
CD
2 = (4 CD / 3 – 21) ∙ 4 CD / 3
CD = (4 CD / 3 – 21) ∙ 4 / 3
9 CD = 16 CD – 21 ∙ 4 ∙ 3
16 CD – 9 CD = 21 ∙ 4 ∙ 3
7 CD = 21 ∙ 4 ∙ 3
CD = 36
Ответ: 36