****Area inside area****

Geometry Level 3

Inradius of circle which is inscribed in a isoceles triangle one of whose angle is 2pi/3 is 3 \sqrt{3} , then area of triangle is

  1. 4 3 4 \sqrt{3}
  2. 12 − 7 3 12 - 7 \sqrt{3}
  3. 12 + 7 3 12 + 7 \sqrt{3}
  4. None of the above.
1 4 2 3

Arpit Dhimanj by Arpit Dhimanj , 23, India

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1 solution

Gwen Roberts
Sep 6, 2015

The triangle is has angles π/6, π/6 and 2π/3. Distance from incenter to vertex of 2π/3 angle is 2, so the altitude of isosceles triangle is 2 + √3, and the base is twice (2 + √3)(2√3+3). The area is 12 +7√3

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Moderator note:

Good observation of using the many 30-60-90 triangles to find the various lengths!

Thank you!

Gwen Roberts - 5 years, 9 months ago

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