Multiple Choice Question (MCQ)

In the figure, each of the three circles is tangent to the other two, and each side of the equilateral triangle is tangent to two of the circles. If the length of one side of the triangle is x, what is the radius, in terms of x, of one of the circles?

  1. ×

    \dfrac{x}{1+2\sqrt{3} }

  2. ✓

    \dfrac{x}{2+2\sqrt{3} }

  3. ×

    \dfrac{x}{1+\sqrt{3} }

  4. ×

    \dfrac{2x}{1+\sqrt{3} }

  5. ×

    \dfrac{2x}{1+2\sqrt{3} }

Steven Zheng posted 3 years ago

Answer

  1. Let r is the radius of the circles, we get the following equation,


    2\cot 30\degree r+2r = x


    2\sqrt{3} r+2r = x


    \therefore r = \dfrac{x}{2+2\sqrt{3} }

Steven Zheng posted 3 years ago

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