Question

prove the perpendicular from centre bisects the chord

Answer 1

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.

OMA and OMB are both right angles.

Triangles OAM and OBM are congruent (RHS), so it follows that AM = MB.

Therefore, M is the midpoint of AB, and the chord has been bisected.

Answer 2

this is the answer along with the diagram