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

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

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 an isosceles ABC, with AB = AC, the bisectors of angleB and angleC intersect each other at O. Joint A to O. Show that: (ii) OB = OC (ii) AO bisects angleA

Quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB+CD=AD+BC .

If the bisector of an angle of a triangle also bisects the opposite side, prove that the triangle is isosceles.

A quadrilateral ABCD is drawn to circumscribe a circle as shown. Prove that AB+CD=AD +BC.

A quadrilateral ABCD is drawn to circumscribe a circle (see Figure).Prove that AB+CD=AD+BC.

ABCD is a quadrilateral in which AD=BC and angleDAB = angleCBA . Prove that: (i) triangleABD ~= triangleBAC (ii) BD = AC (iii) angleABD = angleBAC

In the given figure angleA= 40^(@) . If bar(BO) and bar(CO) are the bisectors of angleB and angleC respectively. Find the measure of angleBOC .