Triangle Inside a Square

For discussing Olympiad level Geometry Problems
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Fahim Shahriar
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Joined:Sun Dec 18, 2011 12:53 pm
Triangle Inside a Square

Unread post by Fahim Shahriar » Sun Mar 02, 2014 5:11 pm

$ABCD$ is a square where $AB=4.$ $P$ is a point inside the square such that $\angle PAB = \angle PBA = 15^\circ.$ $E$ and $F$ are the midpoints of $AD$ and $BC$ respectively. $EF$ intersects $PD$ and $PC$ at points $M$ and $N$ respectively.

$Q$ is a point inside the quadrilateral $MNCD$ such that $\angle MQN = 2 \angle MPN.$ The perimeter of $\triangle MNQ$ is $4$. $PQ=?$
Name: Fahim Shahriar Shakkhor
Notre Dame College

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Raiyan Jamil
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Joined:Fri Mar 29, 2013 3:49 pm

Re: Triangle Inside a Square

Unread post by Raiyan Jamil » Thu Oct 02, 2014 8:32 pm

I think PQ=2.19615........
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