选择题

2005 AMC 8 Problem 23: Semicircle in Right Triangle

Isosceles right triangle ABC encloses a semicircle of area 2π. The circle has its center O on hypotenuse AB and is tangent to sides AC and BC. What is the area of triangle ABC?

A.
6
B.
8
C.
3π
D.
10
E.
4π