Let the center oof the circle be oand the radius be r
let n be a point on a circle through witch cord ab passes and n is the mid point of ab
let another chord cdalso passes through n.
we need to prove that cd > ab
draw om perpenducular to cd and join on.
in right triangle omn,we have
ON > OM since ON is the hypotenus
thus chord cd is closer to o as comper to chord ab
Thus, CD > AB ..... proved