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题库 / OG2017Q-DS-280
The circular base of an above-ground swimming pool lies in a level yard and just touches two straight sides of a fence at points A and B, as shown in the figure above. Point C is on the ground where the two sides of the fence meet. How far from the center of the pool's base is point A ?
(1) The base has area 250 square feet.
(2) The center of the base is 20 feet from point C.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
题目分析：
本题求圆的半径。
（1） 条件1给出圆的面积为250平方英尺，所以根据圆的面积公式~$πr^2=250$~即可解得r，即A点到中心的距离。题目得解。
（2） 条件2给出CQ的长为20英尺，CA为圆的切线，根据定理“切线垂直于过切点的半径”，所以CA和QA垂直，但只有条件2不能得知CA的长，也就无法通过勾股定理求得QA的长。
因此，本题答案为（A），仅条件1可以解题，条件2不行。
CA为圆的切线，根据定理“切线垂直于过切点的半径”，