The tangents to the circle at B and C meet at the point A. A point P is located on the minor arc BC and the tangent to the circle at P meets the lines AB and AC at the points D and E, respectively. Prove that
$$\angle DOE = \frac 12 \angle BOC$$
where O is the center of the given circle.
How should I start this question? What identities or theorems should I use?
Thanks in advance for helping me out.