Circle Around 3 Squares

The radius of the smallest circle containing the symmetric figure composed of the three squares shown at the right is:

  1. 2
  2. 1.25
  3. 1.25
  4. 5√17
  5. none of these

Show/Hide Solution

We’ll design a circle that passes through A, B, C, and D. Its center will be at O, on the line bisecting the symmetric figure, and its radius will be x.

We see that x is the hypotenuse of two right triangles, OEB and OFC. Let OF = t. Then OE = 1 + (1 – t) = 2 – t.

We see that x is approximately 1.29, which is not too different from answer choice (c), but (d) is the exact answer.

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