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 ...

Publications of the Astronomical Society of the Pacific, Vol. 117, No. 833 (July 2005), pp. 711-720 (10 pages) ABSTRACT The shape of the line bisector for the prototype spectral line Fe i λ6253 was ...

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.