Question

The perpendicular from the centre of a circle to a chord bisects the chord. proof

Answer 1

This is solution hope it may helps you

Answer 2

Given :

A perpendicular is drawn from the centre of a circle to the chord

To Find :

To prove that a perpendicular from the centre of a circle to a chord bisects the chord.

Solution :

In triangle OAC and OBC,

      ∠OCA = ∠OCB    (both angles are 90°)

          OA  =  OB   (Radius of the circle)

          OC  =  OC   (common)

∴    ΔOAC ≅  ΔOBC

∴        AC  =  BC   (Congruent parts of congruent triangles are equal)

Thus, C is the midpoint of the chord.

Therefore, the perpendicular drawn from the centre of a circle to a chord bisects the chord.

Hence proved.