Question

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.

• A. True
• B. False

Answer 1

The correct option is B

False

Steps of construction:

• In the given triangle, draw the angle bisector of angle A.

(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. So in order to find the locus of a point which is equidistant from AB and AC, we draw angle bisector of angle A).

• Draw the perpendicular bisector of BC which intersects the angle bisector at P.

(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. So in order to find the locus of a point which is equidistant from B and C, we draw a perpendicular bisector of BC).

P is the required point which is equidistant from AB and AC as well as from B and C.

As we see in the figure above, point P lies outside the considered triangle.

Hence the given statement is false.