In triangle LMN, bisector of interior angles at L and N intersect each other at point A. Prove that :
point A is equidistant from all the three sides of the triangle.

In triangle LMN, bisector of interior angles at L and N intersect each other at point A. Prove that : AM bisects angle LMN.

In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

The bisectors of angleB and angleC of a quadrilateral ABCD intersect each other at point P. Show that P is equidistant from the opposite sides AB and CD.

In triangle ABC,the bisector of interior angle A and the bisector angle C meet at point O. Prove that angle AOC=(1)/(2)angleB

In parallelogram ABCD, the bisectors of adjacent angles A and D intersect each other at point P. prove that angleAPD=90^(@) .

In a parallelogram ABCD, the bisectors of angleA and angleB intersect each other at point P. Prove that angleAPB=90^(@).

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.

A B C is a triangle. The bisector of the exterior angle at B and the bisector of /_C intersect each other at D . Prove that /_D=1/2/_A .

In Delta ABC , AB = AC and the bisectors of angles B and C intersect at point O. Prove that : (i) BO = CO (ii) AO bisects angle BAC.

The coordinates of the point which is equidistant from the three vertices of the triangle AOB as shown in the figure is