Search found 3 matches
- Thu Dec 31, 2020 1:00 pm
- Forum: Geometry
- Topic: Iranian Geometry Olympiad 2020 (Elementary) P1
- Replies: 1
- Views: 6070
Re: Iranian Geometry Olympiad 2020 (Elementary) P1
At first I will fold $AB$.Then,a part will go over $AE$.So I will fold $AC$ such that the part goes under $AE$.Next, I will fold $DE$ such that the upper part of $DE$ goes under $AE$.But a part will go under $BF$.So, I should fold such that the part stays between $BF$ and $AE$.For this, I will fold ...
- Thu Dec 10, 2020 12:16 pm
- Forum: Geometry
- Topic: A Nice Geometry
- Replies: 0
- Views: 6683
A Nice Geometry
Let $ABC$ be an isosceles triangle with base $AC$. Points $D$ and $E$ are chosen on the sides $AC$ and $BC$, respectively, such that $CD = DE$. Let $H, J,$ and $K$ be the midpoints of $DE, AE,$ and $BD$, respectively. The circumcircle of triangle $DHK$ intersects $AD$ at point $F$, whereas the circu...
- Tue Dec 08, 2020 2:22 pm
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: APMO 2020 P1
- Replies: 1
- Views: 5217
Re: APMO 2020 P1
By angle chasing,
$\angle EAC=\angle B= \angle EAD$
So $ACED$ is cyclic and by radical axis theorem on $(ACBF),(EDBF),(ACED)$ we are done.
$\angle EAC=\angle B= \angle EAD$
So $ACED$ is cyclic and by radical axis theorem on $(ACBF),(EDBF),(ACED)$ we are done.