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.
(ii) Construct the locus of points, inside the circle, that are equidistant from AB and AC.

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.
(ii) Construct the locus of points, inside the circle, that are equidistant from AB and AC.

KnowledgeBoat · Accepted Answer

Steps of construction : 1. Construct a circle with center as O and radius 4 cm. 2. Take a point A on the circle. From A make arcs of radius 6 cm and 5 cm and where they intersect the circle mark those points as B and C respectively. (i) We know that locus of points that are equidistant from two points is the perpendicular bisector of line segment joining those points. So from figure, IH is the locus of points inside the circle, that are equidistant from A and C. Hence, the locus is the diameter of the circle which is perpendicular to the chord AC. Proof: Consider △GPA and △GPC. ∠PGC = ∠PGA (Both are equal to 90°) PG = PG (Common side) CG = AG (They are equal as GH bisects AC). Hence, by SAS axiom △GPA congruent to △GPC. Since triangles are similar, hence the ratio of their corresponding sides are equal. Hence, proved that AP = PC. (ii) We know that locus of points that are equidistant from two lines is the angular bisector of the lines. So, from figure, AZ is the angular bisector of angle between AB and AC. AJ is the locus of points equidistant from AB and AC inside the circle. Hence, locus is the chord of the circle bisecting ∠BAC.

Mathematics

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.
(ii) Construct the locus of points, inside the circle, that are equidistant from AB and AC.

Locus

Related Questions

Using ruler and compasses only, construct a quadrilateral ABCD in which AB = 6 cm, BC = 5 cm, ∠B = 60°, AD = 5 cm and D is equidistant from AB and BC.

Using ruler and compasses only, construct a parallelogram ABCD in which AB = 5.1 cm, diagonal AC = 5.6 cm and diagonal BD = 7 cm. Locate the point P on DC, which is equidistant from AB and BC.

A and B are fixed points 5 cm apart. The locus of the point P is the set of those points for which AP = 4 cm and the locus of Q is the set of those points for which BQ = 3.5 cm.
Construct the loci of P and Q and the points of intersection of the two loci. How many such points are there?

Using only a ruler and compasses, construct ∠ABC = 120°, where AB = BC = 5 cm.
(a) Mark two points D and E which satisfy the condition that they are equidistant from both BA and BC.
(b) In the above figure, join AE and EC. Describe the figures.
(i) ABCD
(ii) BD
(iii) ABE

Mathematics

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.(ii) Construct the locus of points, inside the circle, that are equidistant from AB and AC.

Locus

Related Questions

Using ruler and compasses only, construct a quadrilateral ABCD in which AB = 6 cm, BC = 5 cm, ∠B = 60°, AD = 5 cm and D is equidistant from AB and BC.

Using ruler and compasses only, construct a parallelogram ABCD in which AB = 5.1 cm, diagonal AC = 5.6 cm and diagonal BD = 7 cm. Locate the point P on DC, which is equidistant from AB and BC.

A and B are fixed points 5 cm apart. The locus of the point P is the set of those points for which AP = 4 cm and the locus of Q is the set of those points for which BQ = 3.5 cm.Construct the loci of P and Q and the points of intersection of the two loci. How many such points are there?

Using only a ruler and compasses, construct ∠ABC = 120°, where AB = BC = 5 cm.(a) Mark two points D and E which satisfy the condition that they are equidistant from both BA and BC.(b) In the above figure, join AE and EC. Describe the figures.(i) ABCD(ii) BD(iii) ABE

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.
(ii) Construct the locus of points, inside the circle, that are equidistant from AB and AC.

A and B are fixed points 5 cm apart. The locus of the point P is the set of those points for which AP = 4 cm and the locus of Q is the set of those points for which BQ = 3.5 cm.
Construct the loci of P and Q and the points of intersection of the two loci. How many such points are there?

Using only a ruler and compasses, construct ∠ABC = 120°, where AB = BC = 5 cm.
(a) Mark two points D and E which satisfy the condition that they are equidistant from both BA and BC.
(b) In the above figure, join AE and EC. Describe the figures.
(i) ABCD
(ii) BD
(iii) ABE