Let ABC be a triangle such that angle C is obtuse. Let D∈[AB] and [DC]⊥[BC]. If m(ABC)=α, m(BCA)=3α, and ∣AC∣−∣AD∣=10, what is ∣BD∣?<spanclass=′latex−bold′>(A)</span>10<spanclass=′latex−bold′>(B)</span>14<spanclass=′latex−bold′>(C)</span>18<spanclass=′latex−bold′>(D)</span>20<spanclass=′latex−bold′>(E)</span>22