Draw a circle of radius 4 cm whose centre is O. Take a point A on the circumference of this circle.
With A as centre and radius 6 cm draw an arc to cut the circumference at B. Join AB.
Then AB is the chord of the circle of length 6 cm.
With A as centre and radius 5 cm draw another arc to cut the circumference at C. Join AC then AC is the chord of the circle of length 5 cm.
With A as centre and a suitable radius, draw two arcs on opposite sides of AC.
With C as centre and the same radius, draw two arcs on opposite sides of AC to intersect the former arcs at P and Q.
Join PQ and produce to cut the circle at D and E.
Join DE. Then chord DE is the locus of points inside the circle that Ls equidistant from A and C.
As chord DE passes through (he centre O of the circle, it is a diameter. To prove the construction take any point S inside the circle on DE.