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.

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.

Following are the steps of Construction:

ML Aggarwal Solutions for Class 10 Chapter 14 Image 36

(i) Taking O as centre and 4 cm radius construct a circle.

(ii) Mark a point A on this circle.

(iii) Taking A and centre and 6 cm radius construct an arc which cuts the circle at B.

(iv) Again with 5 cm radius, construct another arc which cuts the circle at C.

(vi) Construct the perpendicular bisector of AC.

now,

any point on it will be equidistant from A and C.

(vii) Construct the angle bisector of ∠A which intersects the perpendicular bisector of AC at the point P.

Therefore,

P is the required locus.

i

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