The bisector of the interior angles `angleB and angle C` of the `DeltaABC`, meet at H. Prove that `angleBHC=90^@+(1)/(2)angleBAC`.

ABCD is a cyclic quadrilateral .The side BC is extended to E .The bisectors of the angles angleBADandangleDCE intersect at the point P .Prove that angleADC=angleAPC .

In the adjacent figure the sides AB and AC of Delta ABC are produced to points E and D respectively. If bisectors BO and CO of angleCBE and angleBCD respectively meet at point O, then prove that angleBOC = 90^(@)-(1)/(2) angleBAC .

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

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

If in triangleABC a=2b and angle A=3 angleB then angleA=

In Delta ABC, angle B le angle C. If the interior bisector of angle BAC be AP and AQbotBC. then prove that angle PAQ=(1)/(2)(angle B-angleC)

If a quadrilateral ABCD, the bisector of angleC angleD intersect at O. Prove that angleCOD=(1)/(2)(angleA+angleB)

In the parallelogram ABCD , AB = 2AD . Prove that the bisectors of the angles angleBAD and angleABC meet at the mid-point of DC at right -angles.

In an isoceles triangle ABC, AB = AC and angleBAC=90^(@) , the bisector of angleBAC intersects the side BC at the point D. Prove that (sec angleACD)/(sin angleCAD)="cosec"^(2)angleCAD.

In triangleABC , angleB is an acute angle and AD botBC . Prove that AC^2= AB^2+BC^2-2BC.BD.