Given : CP is bisector of angle C of `DeltaABC`.

Prove : P is equidistant from AC 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: 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 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.

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.

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 the adjoining figure, DeltaABC is an isosceles triangle in which AB = AC. Side CP is parallel to AB and AP is the bisector of exterior angle CAD of Delta ABC. Prove that anglePAC=angleBCAand squareABCP is a parallelogram.

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.

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, with AB = 6 cm, BC = 7 cm and angleABC = 60^@ . Locate by construction the point P such that (i) P is equidistant from B and C (ii) P is equidistant from AB and BC. (iii) Measure and record the length of PA.