## Search found 282 matches

Wed Jan 30, 2019 12:10 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2011 Problem 1
Replies: 1
Views: 266

### Re: APMO 2011 Problem 1

viewtopic.php?f=15&t=1003&p=4148&hilit= ... %2F1#p4148
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Fri Dec 01, 2017 9:29 pm
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 110
Views: 11316

A probelm is posted twice. So, actually this is the number 50. Problem 50: Let the incircle touches side $BC$ of a triangle $\triangle ABC$ at point $D$. Let $H$ be the orthocenter of $\triangle ABC$ and $M$ be the midpoint of segment $AH$. Let $E$ be a point on $AD$ so that $HE \perp AD$. Let $ME \... Mon Nov 20, 2017 12:32 pm Forum: Geometry Topic: Geometry Marathon : Season 3 Replies: 110 Views: 11316 ### Re: Geometry Marathon : Season 3 Problem 47: Let$ABCD$be a cyclic quadrilateral.$AB$intersects$DC$at$E$.$AD$intersects$BC$at$F$. Let$M, N, P$are midpoints of$BD, AC, EF$respectively. Prove that$PN.PM=PE^2$Tue Oct 31, 2017 12:01 am Forum: Geometry Topic: Geometry Marathon : Season 3 Replies: 110 Views: 11316 ### Re: Geometry Marathon : Season 3$\text{Problem 45}$Let$ABC$be a triangle with orthocentre$H$and circumcircle$\omega$centered at$O$. Let$M_a,M_b,M_c$be the midpoints of$BC,CA,AB$. Lines$AM_a,BM_b,CM_c$meet$\omega$again at$P_a,P_b,P_c$. Rays$M_aH,M_bH,M_cH$intersect$\omega$at$Q_a,Q_b,Q_c$. Prove that$P_aQ_a,P_...
Tue Sep 05, 2017 12:25 am
Forum: Algebra
Topic: Sequence and divisibility
Replies: 2
Views: 731