kerem2611 0 Posted April 24 Share Posted April 24 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. Link to post Share on other sites

mathematic 104 Posted April 24 Share Posted April 24 Draw a picture! Link to post Share on other sites

kerem2611 0 Posted April 25 Author Share Posted April 25 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 Link to post Share on other sites

mathematic 104 Posted April 25 Share Posted April 25 The link appears to be a list of numbers - no picture? Link to post Share on other sites

Country Boy 69 Posted June 1 Share Posted June 1 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 Link to post Share on other sites

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