Question

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

$16$

$24$

$32$

$64$

$128$

Solution:

Each circle has diameter $4.$ The short side of the rectangle equals one diameter, so it is $4.$

Since the circle at $Q$ passes through $P$ and $R,$ all three circles have radius $2,$ and the long side spans two full diameters: $4 + 4 = 8.$ The area is $8 \times 4 = 32.$

Thus, the correct answer is C .

1995 AMC 8 Problem 9

Solution:

Problem 9 in Other Years