141. N is interior <==> 1/3<a/b<3 (CRUX Mathematicorum).

by Virgil Nicula, Oct 4, 2010, 6:45 AM

Let $ABCD$ be a trapezoid with $BC\parallel AD$ . Denote $AD=a$ , $BC=b$ , the midpoints $M$ , $P$ , $Q$ of $[CD]$ , $[AM]$ , $[BM]$

respectively and $N\in DP\cap CQ$ . Prove that $N$ belongs to the interior of the triangle $ABM\ \iff\ \frac ab\in\left(\frac 13,3\right)$ .[/quote]
Proof.
This post has been edited 6 times. Last edited by Virgil Nicula, Dec 1, 2015, 11:06 AM

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