In \triangle A B C, A B=B C, and \overline{B D} is an altitude. Point E is on the extension of \overline{A C} such that B E=10. The values of \tan \angle C B E, \tan \angle D B E, and \tan \angle A B E form a geometric progression, and the values of \cot \angle D B E, \cot \angle C B E, \cot \angle D B C form an arithmetic progression. What is the area of \triangle A B C ?
Answer Choices
A. 16
B. \dfrac{50}{3}
C. 10 \sqrt{3}
D. 8 \sqrt{5}
E. 18