Construct the bisector of a given angle /_ ABC=60^@ .

Delta ABC is inscirbed in a circle, the bisector of the angles angle BAC, angle ABC and angle ACB intersect at the point X,Y,Zon the circle repectively. Prove that in Delta XYZ , angle YXZ=90^(@)-(1)/(2) angle BAC

In DeltaABC , the point at which the bisectors of the angles /_ABC and /_BAC intersect is called the incentre of the triangle.

In the adjoining figure, BX and CY are the bisectors of angle ABC and angle ACB respectively. If AB=AC and BY=4 cm, then find the lengths of AX.

In Delta ABC,AB= AC, BE and CF are resepectively the bisectors of angle ABC and angle ACB and itersect the sides AC and AB at the points E and F resepectively. Then four points B,C,E,F are not concylic.

In the adjoining figure, QS is the bisector of an angle angle PQR , if angle SQR=35^(@) and angle PRQ=32^(@) , then find the value of angle QSR .

In a parallelogram ABCD, the bisectors of the consecutive angles angleA and angleB intersect at P. Show that angleAPB=90^(@) .

Prove analytically that the bisectors of the interior angles of a triangle are concurrent.