top of page

P3: Given ABC inscribed in (O) and bisector BD. M is the midpoint of BC. J is a point on AM such that JD is perpendicular to BC. Prove that (J, JD) and Euler-circle touch. 

Screenshot 2023-06-20 171507.png
Screenshot 2023-06-20 174016.png

P4: Given triangle ABC. P is an arbitrary point on the median AM. (APB) intersects AC at E. (APC) intersects AB at F. EF intersects BC at G. (AEF) intersects AM at T. Prove that TG touches (AEF). 

Screenshot 2023-06-20 180614.png
Screenshot 2023-06-20 184925.png

P6:  Given ABC inscribed in (O) with the orthocenter H. M,N,P are respectively midpoints BC,CA,AB. AD,BE,CF are, respectively, heights of triangle ABC. K is the reflection of H through BC. DE intersects MP at X and DF intersects MN at Y. XY intersects arc BC at Z. Prove that K,Z,E,F lies on one circle. 

Screenshot 2023-06-20 205049.png
Screenshot 2023-06-20 210617.png
bottom of page