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 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.

If bisectors of angleA and angleB of a quadrilateral ABCD intersect each other at P, of angleB and angleC at Q, of angleC and angleD of R and of angleD and angleA at S, then PQRS is a (A) Rectangle (B) Rhombus (C) Parallelogram (D) Quadrilateral whose opposite angles are supplementary

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.

The bisectors of angleB and angleC of an isosceles triangle with AB = AC intersect each other at a point O. BO is produced to meet AC at a point M. Prove that angleMOC = angleABC.

Bisectors of angles A and D of a quadrilateral ABCD meet at P. Prove that angleAPD=(1)/(2)(angleB+angleC)

The locus of a point on rhombus ABCD, so that it is equidistant from AB and BC

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

Diagonals of a quadrilateral ABCD bisect each other. If angleA=35^(@), determine angleB .

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.

The diagonals of a quadrilateral ABCD intersect each other at the point O such that (A O)/(B O)=(C O)/(D O) . Show that ABCD is a trapezium.