I had this task on my math test:
In the triangle ABC, the bisector of angle at C intersects side AB at point D. Given that the angle at C is 120°, |AB| = 6cm and |BC| = 12cm, calculate the length of bisector |CD|.
I think that such a triangle cannot exist. In every triangle, the largest side is opposite of the largest angle. Thus, as |BC] > |AB|, the angle at A must be greater than the angle at C, which is 120°. From there it follows that the sum of angles in this triangle is larger than 180°, which is impossible.
I am not sure if this makes the task unsolvable...
I would appreciate if you help me solve it or tell me it is impossible to solve (could be that the author made a mistake, e.g. he meant |DB|, not |AB| or something).