Area of a Triangle Just From a Circle?

Geometry Level 4

The given triangle is isosceles with vertex angle $120^\circ$ and inradius of length $\sqrt{3}.$ In simplest form, the area of the triangle is $a + b\sqrt{c}.$ Find $a+b+c.$

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Area of a Triangle Just From a Circle?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.