单选题
In the figure at the right, the legs of fight triangle ACB are diameters of the two semicircles. If AB = 4, what is the sum of the areas of the semicircles?
【正确答案】
B
【答案解析】Let x and y be the radii of the two semicircles. Then the legs of right triangle ACB fire 2x and 2v, and by the Pythagorean theorem (2-x)2 + (2y)2 = 42. Then 4x2 + 4y2 = 16, and x2 + y2 = 4. Since the area of a semicircle of radius r is [*], the sum of the areas of the semicircles is
[*]
**Use TACTIC 2, Chapter 11. Pick numbers a and b for the legs of the triangle. For exam- ple, if a is 2, then by the Pythagorean theorem 22 + b2 = 42.
[*]
[*]
**Use TACTIC 2, Chapter 11. Pick numbers a and b for the legs of the triangle. For exam- ple, if a is 2, then by the Pythagorean theorem 22 + b2 = 42.
[*]