Let ABC be an acute triangle with ∣AB∣=∣AC∣ and the midpoints of segments [AB] and [AC] be D resp. E. The circumcircles of the triangles BCD and BCE intersect the circumcircle of triangle ADE in P resp. Q with P=D and Q=E.
Prove ∣AP∣=∣AQ∣.(Notation: ∣⋅∣ denotes the length of a segment and [⋅] denotes the line segment.) geometrycircumcircleIntersection