ABCD is a quadrilateral in which AB= AD, the bisector of `angle BAC and angle CAD` intersect the sides BC and CD at the points E and F respectively. Prove that EF || BD.

O is any point inside a triangle ABC. The bisector of angle AOB, angle BOC and angle COA meet the sides AB, BC and CA in point D, E and F respectively. Show that AD xx BE xx CF= DB xx EC xx FA

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

In a cyclic quadrilateral ABCD, the bisectors of opposite angles A and C meet the circle at Pand Q respectively. Prove that PQ is a diameter of the circle.

ABC is right - angled triangle at B. Let D and E be any two point on AB and BC respectively . Prove that AE^2 + CD^2 = AC^2 + DE^2

In A B C , the bisector of the angle A meets the side BC at D andthe circumscribed circle at E. Prove that D E=(a^2secA/2)/(2(b+c))

ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram.

In A B C , the three bisectors of the angle A, B and C are extended to intersect the circumeircle at D,E and F respectively. Prove that A DcosA/2+B EcosB/2+C FcosC/2=2R(sinA+sinB+sinC)

In the adjoint figure, AD is the bisector of the exterior angleA" of "DeltaABC. Seg AD intersects the side BC produced in D. Prove that : (BD)/(CD)=(AB)/(AC)

In a triangle ABC, D is a point on BC such that AD is the internal bisector of angle A . Let angle B = 2 angle C and CD = AB. Then angle A is

In the adjoining figure,seg AB is a diameter of a circle with centre O . Bisector of inscribed angleACB intersects circle at point D. Complete the following proof by filling in the blanks. Prove that : seg AD ~= seg BD