[" Bisectors of angles "A,B" and "C" of a triangle ABC intersect its circumcircle at "D" ,Eand Fespectively."],[" Prove that the angles of "/_DEF" are "90-(A)/(2),90-(B)/(2)" and "90-(C)/(2)]

Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are 90o-1/2A , 90o-1/2B and 90o-1/2C

Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are 90o-1/2A ,90o-1/2B and 90o-1/2C

Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are 90^@-1/2A , 90^@-1/2B and 90^@-1/2C

Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are 90^@-1/2A , 90^@-1/2B and 90^@-1/2C

Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that angles of the triangle are 90^@-A/2,90^@-B/2 and 90^@-C/2 respectively.

Bisectors of vertex angles A, B and C of a triangle ABC intersect its circumcircle at the points D,E and F respectively. Prove that angle EDF=90^(@)-1/2/_A

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

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

The internal bisectors of the angles of a triangle ABC meet the sides in D, E, and F. Show that the area of the triangle DEF is equal to (2/_\abc)/((b+c)(c+a)(a+b) , where /_\ is the area of ABC.