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Lines, Angles, and Triangles

SAT Math· difficulty 4/5

A circle is inscribed in an equilateral triangle of side length 12. What is the radius of the inscribed circle?

  • A

    434\sqrt{3}

  • B

    232\sqrt{3}

    check_circle
  • C

    66

  • D

    33

Explanation

For an equilateral triangle: inradius r=fracssqrt36=frac12sqrt36=2sqrt3r = \\frac{s\\sqrt{3}}{6} = \\frac{12\\sqrt{3}}{6} = 2\\sqrt{3}.

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