Question

A triangle has sides with lengths of 1, 9, and 8. What is the radius of the triangles inscribed circle?

Answer 1

No such triangle exists, since `1+8>9` is untrue.

Explanation:

The triangle inequality theorem states that for any triangle with sides `a,b,c`

`a+b>c`

`b+c>a`

`c+a>b`

Here, this is broken in the case of `1+8>9`.