Question 77
Let $ABC$ be an isosceles triangle with base $BC = 10$ and $AB = AC$. On its two legs, two further isosceles triangles $DAB$ and $EAC$ are constructed externally, both similar to $ABC$, with $DA = DB$ and $EA = EC$. Given that $DE = 45$, find the length of $AB$.
(A) 15
(B) 20
(C) $9\sqrt{5}$
(D) 22.5
(E) It cannot be determined from the given data alone.
(A) 15
(B) 20
(C) $9\sqrt{5}$
(D) 22.5
(E) It cannot be determined from the given data alone.