kerem2611
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Posts posted by kerem2611
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12 hours ago, mathematic said:
Draw a picture!
I already have, click on the link please
12 hours ago, mathematic said:Draw a picture!
my sketch: https://www.geogebra.org/classic/hgyxdyxu
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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 andcuts 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 theline EF at some point that lies on the circumcircle of triangle DLG.0
Olympiad question (prove)
in Applied Mathematics
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