(Converse of Theorem 3) The line joining the centre of a circle to the mid-point of a chord is perpendicular to the chord.

Explanation

Given chord `PQ`,`L` is the mid point of `PQ`
`PL=LQ`
To proof:-
`angle OLQ=angle OLP=90^0`
In `triangle OPL` and `triangleOQL`
`OP=OQ`....[radius]
`OL=OL`.....[common]
`PL=LQ`.....[given]
By `SSS` congranency `triangleOLP~=triangle OLQ`
`angle OLQ=angle OLP`
`angle OLP+angleOLQ=180^0`
`angleOLP+angleOLP=180^0`
`2angleOLP=180^0`
`angleOLP=90^0`
`angleOLQ=angleOLP=90^0`