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

AMC 8 2005 Problem 23

AMC8 2005 年第 23 题

三角形★★★★☆

Isosceles right triangle ABC encloses a semicircle of area 2\pi. The circle has its center O on hypotenuse \overlineAB and is tangent to sides \overlineAC and \overlineBC. What is the area of triangle ABC?

等腰直角三角形 ABC 内包含了一个面积为 2π的半圆，圆的圆心在斜边相切。则三角形 ABC 的面积是多少？上，且和边，

A.6
B.8
C. $3\pi$
D.10
E. $4\pi$

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