If x, y, z be the lengths of the internal bisectors of the angles of a triangle l,m,n be the lengths of these bisectors produced to meet the circumcircle, then show that `l cos(A/2)+m cos (B/2)+n cos (C/2)=a+b+c`

If x,y,z be the lengths of the internal bisectors of the angles of a triangle 1,m,n be the lengths of these bisectors produced to meet the circumcircle,then show that x^(-1)cos((A)/(2))+y^(-1)cos((B)/(2))+z^(-1)cos((C)/(2))=a^(-1)+b^(-1)+c^(-1)

In DeltaABC with fixed length of BC , the internal bisector of angle C meets the side AB at D and meet the circumcircle at E. The maximum value of CD xx DE is

In DeltaABC , the bisectors of the angles A, B and C are extended to intersect the circumcircle at D,E and F respectively. Prove that AD cos.(A)/(2) + BE cos.(B)/(2) + CF cos.(C)/(2) = 2R (sin A + sin B + sin C)

If A, B, C are interior angle of triangle ABC then show that sin ((A+B)/2) + cos (( A+ B)/2) = cos (C/2) + sin (C/2)

Let ABC be a triangle inscribed in a circle and let l_(a)=(m_(a))/(M_(a)), l_(b)=(m_(b))/(M_(b)), l_(c )=(m_(c ))/(M_(c )) where m_(a), m_(b), m_(c ) are the lengths of the angle bisectors of angles A, B and C respectively , internal to the triangle and M_(a), M_(b) and M_(c ) are the lengths of these internal angle bisectors extended until they meet the circumcircle. Q. l_(a) equals :

If one of the angles A,B,C of a triangle is not acute, show that cos^2A+cos^2B+cos^2C=1