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`

In DeltaABC, AB = AC and the bisectors of angleB and angleC meet AC and AB at point D and E respectively. Prove that BD = CE .

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

In Triangle A B C with fixed length of B C , the internal bisector of angle C meets the side A B a tD and the circumcircle at E . The maximum value of C D×D E is c^2 (b) (c^2)/2 (c) (c^2)/4 (d) none of these

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

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.

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 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 triangle A B C ,/_A=60^0,/_B=40^0,a n d/_C=80^0dot If P is the center of the circumcircle of triangle A B C with radius unity, then the radius of the circumcircle of triangle B P C is (a) 1 (b) sqrt(3) (c) 2 (d) sqrt(3) 2

If the bisector of the vertical angle of a triangle bisects the base of the triangle. then the triangle is isosceles. GIVEN : triangle A B C in which A D is the bisector of angle A meeting B C in D such that B D=DC TO PROVE : triangleA B C is an isosceles triangle.