Multiple choice

A circle of radius unity is inscribed in an isosceles triangle. The least perimeter of the triangle is

  1. $6\sqrt{3}$
  2. $9$
  3. $2\sqrt{3}$
  4. $3\sqrt{3}$
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A Correct answer
Explanation

For a circle of radius r inscribed in a triangle, the area A = rs, where s is the semi-perimeter. For a fixed r, the perimeter is minimized when the triangle is equilateral. For r=1, the side length of an equilateral triangle is 2*sqrt(3), so the perimeter is 6*sqrt(3).

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