AMC8 1995

AMC8 1995 · Q9

AMC8 1995 · Q9. It mainly tests Triangles (properties), Area & perimeter.

Three congruent circles with centers P, Q and R are tangent to the sides of rectangle ABCD as shown. The circle centered at Q has diameter 4 and passes through points P and R. The area of the rectangle is

三个全等的圆，以 P、Q 和 R 为圆心，如图所示，与矩形 ABCD 的边相切。以 Q 为圆心的圆直径为 4，并经过点 P 和 R。矩形的面积是

(A) 16 16

(B) 24 24

(D) 64 64

(E) 128 128

Answer

Correct choice: (C)

正确答案：（C）

Solution

The length of BC is the same as the diameter of the circle with center Q, so BC = 4. The diameters of the circles with centers P and R are also 4. The sum of the diameters of the circles with centers P and R gives the length of AB, so AB = 4 + 4 = 8. Hence the area of the rectangle is 8 × 4 = 32.

BC 的长度与以 Q 为圆心的圆的直径相同，因此 BC = 4。以 P 和 R 为圆心的圆的直径也是 4。以 P 和 R 为圆心的圆直径之和给出 AB 的长度，因此 AB = 4 + 4 = 8。因此矩形的面积是 8 × 4 = 32。

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