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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.
 
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  • 1 month later...
On 4/24/2021 at 7:46 AM, kerem2611 said:
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. 
[/quote]
.
 

An acute scalene triangle.  Depending on exactly how "isosceles" is defined (it variies) saying a triangle is "non-isosceles" might include equilateral triangles

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