Need help with this, if it is true or false and why.

"If a circle with its centre at the origin has a chord with slope m, the equation of the right bisector of the chord is "y=mx".

Is this statement true or false, and can you give me detailed reasons for your answer.

I have been re reading my notes and going thru my books and I can not figure this out at all.

Can someone help me on this please, and thanks for your reply.

Joanne