Question 30
In an acute triangle $ABC$, points $D$ and $E$ lie on sides $AB$ and $AC$ respectively which satisfy $BD = CE$. Point $P$ is on line segment $DE$ and point $Q$ lie on arc $BC$, not containing $A$, of the circumcircle of triangle $ABC$. These points satisfy $BP : PC = EQ : QD$ and points $A, B, C, D, E, P, Q$ are all distinct. Show that $\angle BPC = \angle BAC + \angle EQD$.
In the above, denote by $XY$ the length of line segment $XY$.
In the above, denote by $XY$ the length of line segment $XY$.