Hi guys, I really need help with this question :/
(my sketch: https://www.geogebra.org/classic/abeyyk7p )
Let ABC be an acute, non-isosceles triangle with D is any point on segment BC.
Take E on the side AB and take F on the side AC such that ∠DEB = ∠DFC.
The lines DF, DE cut AB, AC at M, N, respectively.
Denote (I1), (I2) as the circumcircle of DEM, DFN.
Let (J1) be the circle that internal tangent to (I1) at D and also tangent to AB at K,
let (J2) be the circle that internal tangent to (I2) at D and also tangent to AC at H.
Denote P as the intersection of (I1) and (I2) that differs from D and also denote Q as the intersection of (J1) and (J2) that differs from D.
(a) Prove that these points D, P, Q are collinear.
(b) The circumcircle of triangle AEF cuts the circumcircle of triangle AHK and
cuts the line AQ at G and L (G, L differ from A).
Prove that the tangent line at D of the circumcircle of triangle DQG cuts the
line EF at some point that lies on the circumcircle of triangle DLG.
