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

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
True

Steps of construction:

Draw a circle with radius 4 cm(mark the centre of the circle as O).

Take a point A on it.

With A as centre and radius 5 cm, draw an arc which intersects the circle at B.

Again, with A as the centre and radius 4 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.

Draw the perpendicular bisector 'm' of AB which intersects AB at N and meets the circle at P and Q.

(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 bisectors of AB and AC so as to get the locus of the point which is equidistant from A and B and locus of the point which is equidistant from A and C respectively).

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

From constructions, we see that the point of intersection of locus of points, inside the circle, that are equidistant from A and C and the locus of points, inside the circle, that are equidistant from A and B, is O, the centre of the circle.

Hence the given statement is true.

Suggest Corrections

Similar questions

Use ruler and compass only for this question
(i) Construct $Δ A B C$ , where AB = 3.5 cm, BC = 6 cm and $∠ A B C = 60^{\circ}$
(ii) Construct the locus of points inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark the point P which is equidistant from AB, BC and also equidistant from B and C.

Then the length of PB is

Describe the locus for questions 1 to 13 given below:

the locus of points inside a circle and equidistant from two fixed points on the circumference of the circle.

In the given triangle ABC, the point of intersection of the locus of a point equidistant from AB and AC and the locus of a point equidistant from B and C lies inside the triangle.

Q. Draw a line

A B = 5 c m

. Mark a point

C

A B

such that

A C = 3 c m

. using a ruler and a compass only construct :
(i) a circle of radius

2.5 c m

passing through

A

and

C

.
(ii) construct two tangents to the circle from the external point

B

.
Measure and record the lengths of the tangents .

Describe:

(i) The locus of points at distances less than 3 cm from a given point.

(ii) The locus of points at distances greater than 4 cm from a given point.

(iii) The locus of points at distances less than 2.5 cm from a given point.

(iv) The locus of points at distances greater than or equal to 35 mm cm from a given point.

(v) The locus of the centre of a given circle which rolls around the outside of a second circle and is always touching it.

(vi) The locus of the centres of all circles that are tangent to both the arms of a given angle.

(vii) The locus of the mid-points of all chords parallel to a given chord of a circle.

(viii) The locus of points within a circle that are equidistant from the end points of a given chord.

Join BYJU'S Learning Program