Question

what's the maximum radius and area can be inscribed in an isosceles triangle with length 1

Answer 1

The largest circle would be when the triangle is equilateral:

Answer 2

The radius happens to be the length from the center of the triangle to the middle of one of the faces.

Answer 3

That length would be 1/3 the height of the triangle.

Answer 4

Thank you very much. I didn't write the question very clearly, sorry. What are the radius and area of the circle of maximum area that can be inscribed in an isosceles triangle whose two sides have length 1? I couldn't figure it out. can you help me?

Answer 5

The height of the triangle is sqrt(3)/2, so the radius of the inscribed circle is sqrt(3)/6