Balkan MO 2014,G5

For discussing Olympiad level Geometry Problems
tanmoy
Posts:312
Joined:Fri Oct 18, 2013 11:56 pm
Location:Rangpur,Bangladesh
Balkan MO 2014,G5

Unread post by tanmoy » Thu Nov 26, 2015 10:55 pm

Let $ABCD$ be a trapezoid inscribed in the circle $\Gamma$ with $AB$ as diameter.$AC\cap BD=E$.The circle with radius $BE$ and center $B$ intersects $\Gamma$ at points $K$ and $L$.Let $M$ be a point so that $M$ lies on $CD$ and $ME\perp BD$.Prove that $KM\perp LD$
"Questions we can't answer are far better than answers we can't question"

rah4927
Posts:110
Joined:Sat Feb 07, 2015 9:47 pm

Re: Balkan MO 2014,G5

Unread post by rah4927 » Fri Dec 04, 2015 6:13 pm

M is the orthocentre of $\Delta DKL$
Another problem related to this configuration:

Prove that $E$ is the incentre of $\Delta DKL$ .

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