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`

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 90o-1/2A , 90o-1/2B and 90o-1/2C

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 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.

The altitude form the vertices A, B and C of the triangle ABC meet its circumcircle at D,E and F, respectively . The complex number representing the points D,E, and F are z_(1),z_(2) and z_(3) , respectively. If (z_(3) -z_(1))//(z_(2) -z_(1)) is purely real, then show that triangle ABC is right-angled at A.

Let the altitudes from the vertices A, B and Cof the triangle e ABCmeet its circumcircle at D, E and F respectively and z_1, z_2 and z_3 represent the points D, E and F respectively. If (z_3-z_1)/(z_2-z_1) is purely real then the triangle ABC is

The given figure shows a triangle ABC with angle BAC= 56 ^(@) and angle ABC = 64^(@) , Bisectors of angles A,B and C meet the circumcircle of the Delta ABC at points P,Q and R respectively . Find the measure of angle QPR .

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 circumcentre of the triangle ABC is O . Prove that angle OBC+angle BAC=90^@ .

In triangle ABC,the bisector of interior angle A and the bisector angle C meet at point O. Prove that angle AOC=(1)/(2)angleB