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

Explanation

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`,
`angleOCA = angleOCB` (both angles are` 90^@`)
`OA = OB ` (Radius of the circle)
`OC = OC` (common)
`triangleOAC cong triangleOBC`
`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.