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 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

The bisectors of the angles B and C of a triangle A B C , meet the opposite sides in D and E respectively. If DE||BC , prove that the triangle is isosceles.

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 bisectors of angles A and B of a scalene triangle ABC meet at O. What is the point O called ?

If the bisector of the angel C of a triangle ABC cuts AB in D and the circumcircle E, prove that CE:DE=(a+b)^2:c^2

The bisectors of angles A and B of a scalene triangle ABC meet at O. What is the relation between angle ACO and angle BCO?

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.

Bisectors of the angles B and C of an isosceles Delta ABC with AB = AC intersect each other at O . Show that external angle adajcent to angleABC is equal to angleBOC.

Diagonals A C and B D of a trapezium A B C D with A B || C D intersect each other at O . Prove that ar ( triangle A O D)=a r( triangle B O C) .