Draw a circle of radius 3 cm and mark two chords AB and AC of the circle of lengths 4 cm and 5 cm respectively, using ruler and compasses only. Then the locus of points, inside the circle, that are equidistant from A and C, passes through the centre of the circle.

True

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False

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Solution

The correct option is A
True

Steps of construction:

Draw a circle with radius 3 cm(mark the centre of the circle as O).

Take a point A on it.

With A as centre and radius 4 cm, draw an arc which intersects the circle at B.

Again, with A as the centre and radius 5 cm, draw an arc which intersects the circle at C.

Join AB and AC.

Draw the perpendicular bisector 'l' of AC which intersects AC at M and meets the circle at E and F.

(We know that the locus of a point which is equidistant from two fixed points is the perpendicular bisector of the line segment joining the two fixed points. We draw the perpendicular bisector 'l' of AC so as to get the locus of the point which is equidistant from A and C).

EF is the locus of points inside the circle which is equidistant from A and C.

From constructions, we see that the locus of points, inside the circle, that are equidistant from A and C, passes through O, which is the centre of the circle.

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