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Perpendicular bisector on a triangle

The red line is the perpendicular bisector of AB. Move vertices A,B and C around a few times, observe what happens and answer the questions below.

Does the perpendicular bisector of AB always have to pass through vertex C?

Move vertices around until the perpendicular bisector passes through C. What type of triangle must ABC be?

When the perpendicular bisector passes through C, line CD is also what type(s) of line?

What information is required to work out the equation of the perpendicular bisector?

The red line is the perpendicular bisector of AB. Move vertices A,B and C around a few times, observe what happens and answer the questions below.