# Use ruler and compasses only for this question.

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Use ruler and compasses only for this question. Draw a circle of radius 4 cm and mark two chords AB and AC of the circle of length 6 cm and 5 cm respectively.
(i) Construct the locus of points, inside the circle, that are equidistant from A and C. Prove your construction.
(ii) Construct the locus of points, inside the circle, that are equidistant from AB and AC.

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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.