An acute, non-isosceles triangle ABC is inscribed in a circle with centre O. A line go through O and midpoint I of BC intersects AB,AC at E,F respectively. Let D,G be reflections to A over O and circumcentre of (AEF), respectively. Let K be the reflection of O over circumcentre of (OBC).
a) Prove that D,G,K are collinear.
b) Let M,N are points on KB,KC that IM⊥AC, IN⊥AB. The midperpendiculars of IK intersects MN at H. Assume that IH intersects AB,AC at P,Q respectively. Prove that the circumcircle of △APQ intersects (O) the second time at a point on AI. geometrycircumcirclegeometric transformationreflection