Now use the information you already have about finding the equation of a line and apply it to the dashed lines shown in these triangles ... The perpendicular bisector passes through the midpoint ...

OM is perpendicular to AB (meet at a right angle). Look at triangles OAM and OBM. The hypotenuses (OA and OB) are the same, as they are both the radius of the circle. OM is common to both triangles.