Multiple choice

$BC, AB$ and $AC$ are tangents to the circle at $D, E$ and $F$ respectively. $\angle EBD=x^{\circ}, \angle FCD=y^{\circ}.$ Then $\angle EDF$ equals

  1. $x+y$
  2. $\displaystyle \frac{x}{2}-y$
  3. $90^{\circ}-\left ( x+y \right )$
  4. $\displaystyle \frac{x+y}{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the properties of tangents from an external point, the angles in the triangle formed by the circle and the tangents relate to the center. The angle EDF is half the sum of the angles at the vertices B and C in the triangle ABC.