Q : 8 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 , and
Given : Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively.
To prove : the angles of the triangle DEF are , and
Proof :
1 and 3 are angles in same segment.therefore,
1 = 3 ................1(angles in same segment are equal )
and 2 = 4 ..................2
Adding 1 and 2,we have
1+2=3+4
,
and
Similarly, and