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)

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

S is the centre of the circumcircle of Delta ABC and if AD bot BC , prove that angle BAD= angle SAC .

O is the circumcentre of Delta ABC and OD bot BC . Prove that angle BOD= angle BAC

If the bisector of angle A of triangle ABC makes an angle theta with BC, then sin theta is

If the angles of the triangle ABC are in A.P. and b:c= sqrt3:sqrt2 then find the value of angleA

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