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∘−12∠A,90∘−12∠B and 90∘−12∠C

Bisectors of angles ∠A,∠B and ∠C of a triangle ABC intersect its

1.	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∘−12∠A,90∘−12∠B and 90∘−12∠C
Answer» Bisectors of angles $∠ A, ∠ B$ and $∠ C$ of a triangle $A B C$ intersect its circumcircle at $D, E$ and $F$ respectively. Prove that the angles of the triangle $D E F$ are $90^{\circ} - \frac{1}{2} ∠ A, 90^{\circ} - \frac{1}{2} ∠ B$ and $90^{\circ} - \frac{1}{2} ∠ C$