Draw a circle of radius 4 cm and mark two chords AB and AC of the circle of lengths 2 cm and 3 cm respectively, using ruler and compasses only. Then the locus of points, inside the circle, that are equidistant from AB and AC, passes through the centre of the circle.
Draw a circle of radius 4 cm and mark two chords AB and AC of the circle of lengths 2 cm and 3 cm respectively, using ruler and compasses only. Then the locus of points, inside the circle, that are equidistant from AB and AC, passes through the centre of the circle.
The correct option is B False
Steps of construction:
- Draw a circle with centre at O and radius 4 cm.
- Take a point A on it.
- With A as centre and radius 2 cm, draw an arc which intersects the circle at B.
- Again, with A as the centre and radius 3 cm, draw an arc which intersects the circle at C.
- Join AB and AC.
- Draw the bisector 'l' of angle at A which meets the circle at E.
(We know that the locus of a point which is equidistant from two intersecting straight lines is a pair of straight lines which bisect the angles between the given lines. We draw the bisector 'l' of angle A so as to get the locus of the point which is equidistant from AB and AC).
AE is the locus of points inside the circle which is equidistant from AB and AC.
From constructions, we see that the locus of points, inside the circle, that are equidistant from AB and AC, does not pass through O, which is the centre of the circle.
False
Steps of construction:
- Draw a circle with centre at O and radius 4 cm.
- Take a point A on it.
- With A as centre and radius 2 cm, draw an arc which intersects the circle at B.
- Again, with A as the centre and radius 3 cm, draw an arc which intersects the circle at C.
- Join AB and AC.
- Draw the bisector 'l' of angle at A which meets the circle at E.
(We know that the locus of a point which is equidistant from two intersecting straight lines is a pair of straight lines which bisect the angles between the given lines. We draw the bisector 'l' of angle A so as to get the locus of the point which is equidistant from AB and AC).
AE is the locus of points inside the circle which is equidistant from AB and AC.
From constructions, we see that the locus of points, inside the circle, that are equidistant from AB and AC, does not pass through O, which is the centre of the circle.
