Given : AX bisects angle BAC and PQ is perpendicular bisector of AC which meets AX at point Y.

Prove : X is equidistant from AB and AC.

The given figure shows a triangle ABC in which AD bisects angle BAC. EG is perpendicular bisector of side AB which intersects AD at point F. Prove that : F is equidistant from AB and AC.

Construct a triangle ABC, in which AB = 4.2 cm, BC = 6.3 cm and AC = 5 cm. Draw perpendicular bisector of BC which meets AC at point D. Prove that D is equidistant from B and C.

In triangle ABC, D is mid-point of AB and CD is perpendiicular to AB. Bisector of angleABC meets CD at E and AC at F. Prove that: F is equidistant from AB and BC.

In triangle ABC, D is mid-point of AB and CD is perpendiicular to AB. Bisector of angleABC meets CD at E and AC at F. Prove that: E is equidistant from A and B

In the figure, BX bisects angle ABC and intersects AC at point D. Line segment CY is perpendicular to AB and intersects BX at point P. If Y is mid-point of AB, prove that : point P is equidistant from A and B.

In the figure, BX bisects angle ABC and intersects AC at point D. Line segment CY is perpendicular to AB and intersects BX at point P. If Y is mid-point of AB, prove that : point D is equidistant from AB and BC.

Construct a triangle ABC which angle ABC=75^(@), AB=5" cm"and BC =6.4" cm" . Draw perpendicular bisector of side BC and also the bisector of angle ACB. If these bisector intersect each other at point P, prove that P is equidistant from B and C, and also from AC and BC.

In parallelogram ABCD, side AB is greater than side BC and P is a point in AC such that PB bisects angle B. Prove that P is equidistant from AB and BC.

In the given figure, ABCD is a square. M is the mid-point of AB and PQ is perpendicular to CM. CB produced meets PQ at point Q. Prove that : (i) PA = BQ (ii) CP = AB + PA

In each of the given figures, PA = PB and QA = QB. Prove, in each case, that PQ (produce, if required) is perpendicular bisector of AB. Hence, state the locus of the points equidistant from two given fixed points.