Wins and fails are not mutually exclusive

by math_explorer, Sep 11, 2010, 7:26 AM

Turns out it was biconditional.
math_explorer wrote:
Suppose $\triangle ABC$ is a triangle and $P$ is a point inside it such that $\angle PAC = \angle PCB = \angle PBA$. Prove that $BP$ bisects $AC$ iff $AB = AC$.

Click to reveal hidden text

The fail was mainly that the last two "iff"s eluded me for maybe half an hour.

(edited in)
Okay, next problem feels like an easy one. APMO 1996.1:
$ABCD$ is a rhombus (*). Points $M \in AD$, $N \in DC$, $P \in AB$, and $Q \in BC$ are such that $MN \perp BD$, $PQ \perp BD$. Prove that, if the distance between $MN$ and $PQ$ is constant, then the perimeter of $AMNCQP$ is constant.

* The book spells out the definition of "rhombus" instead of using the word.
This post has been edited 4 times. Last edited by math_explorer, Sep 11, 2010, 12:07 PM
geo problem
geometry

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