Triangle ABC is isosceles, with AB=BC=1 and angle ABC equal to 120°. A circle is tangent to the line AB at A and to the line BC at C.
What is the radius of the circle?
[You should state clearly any geometrical facts or theorems you use in each step of your calculation. For example, if one of your steps calculates the size of an angle in a triangle you might justify that particular step with "because angles in a triangle add up to 180 degrees."]
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