## Search found 81 matches

Mon Jan 09, 2017 2:59 pm
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 146
Views: 63396

### Re: Geometry Marathon : Season 3

Now, an easy.problem :D Problem 12: Let $\triangle ABC$ be scalene, with $BC$ as the largest side. Let $D$ be the foot of the perpendicular from $A$ on side $BC$. Let points $K,L$ be chosen on the lines $AB$ and $AC$ respectively, such that $D$ is the midpoint of segment $KL$. Prove that the points ...
Mon Jan 09, 2017 12:15 am
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 146
Views: 63396

### Re: Geometry Marathon : Season 3

Problem 11 : Let $ABC$ be a triangle inscribed circle $(O)$, orthocenter $H$. $E,F$ lie on $(O)$ such that $EF\parallel BC$. $D$ is midpoint of $HE$. The line passing though $O$ and parallel to $AF$ cuts $AB$ at $G$. Prove that $DG\perp DC$. Solution of problem 11 : We first denote some extra point...
Fri Jan 06, 2017 8:59 pm
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 146
Views: 63396

### Re: Geometry Marathon : Season 3

Problem 4: Let $ABC$ be a triangle and $m$ a line which intersects the sides $AB$ and $AC$ at interior points $D$ and $F$, respectively, and intersects the line $BC$ at a point $E$ such that $C$ lies between $B$ and $E$. The parallel lines from the points $A$, $B$, $C$ to the line $m$ intersect the...
Fri Jan 06, 2017 8:19 pm
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 146
Views: 63396

### Re: Geometry Marathon : Season 3

$\text{Problem 3:}$ In Acute angled triangle $ABC$, let $D$ be the point where $A$ angle bisector meets $BC$. The perpendicular from $B$ to $AD$ meets the circumcircle of $ABD$ at $E$. If $O$ is the circumcentre of triangle $ABC$ then prove that $A,E$ and $O$ are collinear. Solution of problem 3 : ...
Fri Jan 06, 2017 7:16 pm
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 146
Views: 63396

### Re: Geometry Marathon : Season 3

Problem 2 In $\triangle ABC$, $\angle ABC=90^{\circ}$. Let $D$ be any point on side $AC$, $D \neq A,C$. The circumcircle of $\triangle BDC$ and the circle with center $C$ and radius $CD$ intersect at $D,E$. Let $F$ be a point on side $BC$ so that $AF \parallel DE$. $X$ is another point on $BC$(Diff...
Thu Jan 05, 2017 11:42 pm
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 146
Views: 63396

### Geometry Marathon : Season 3

$\Re$evived $\Re$ules : Let's revive geo marathon (after 6 yrs only :mrgreen: ) . The rules will be almost same as before, just enhance solving time duration for 2 days . The difficulty level should be around G1-G5 compared with ISL(IMO Shortlist). Solver will post his own solution of the former pr...
Thu Jan 05, 2017 10:16 pm
Forum: Geometry
Topic: GEOMETRY MARATHON: SEASON 2
Replies: 11
Views: 5443

### Re: GEOMETRY MARATHON

Next thread goes to the following page :

viewtopic.php?f=25&t=3802
Thu Jan 05, 2017 7:29 pm
Forum: Geometry
Topic: GEOMETRY MARATHON: SEASON 2
Replies: 11
Views: 5443