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		<title>Problem 1.</title>
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		<pubDate>Wed, 23 Jul 2008 23:53:23 +0000</pubDate>
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				<category><![CDATA[Problems for Jounals]]></category>

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		<description><![CDATA[Let two points interior to the circle such that is the midpoint of Let an arbitrary point lies on and the second intersections of the lines with respectively. The tangents in with respect to the circle intersect each other at Prove that the perpendicular bisector of the segment passes through the midpoint of (Mathematical Reflections [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=tahongson.wordpress.com&amp;blog=4308847&amp;post=4&amp;subd=tahongson&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>Let <img src='http://s0.wp.com/latex.php?latex=M%2C%5C%2CN&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='M,&#92;,N' title='M,&#92;,N' class='latex' /> two points interior to the circle <img src='http://s0.wp.com/latex.php?latex=%5Cmathcal%7BC%7D%28O%29&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='&#92;mathcal{C}(O)' title='&#92;mathcal{C}(O)' class='latex' /> such that <img src='http://s0.wp.com/latex.php?latex=O&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='O' title='O' class='latex' /> is the midpoint of <img src='http://s0.wp.com/latex.php?latex=MN.&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='MN.' title='MN.' class='latex' /> Let <img src='http://s0.wp.com/latex.php?latex=S&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='S' title='S' class='latex' /> an arbitrary point lies on <img src='http://s0.wp.com/latex.php?latex=%5Cmathcal+C%28O%29%2C&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='&#92;mathcal C(O),' title='&#92;mathcal C(O),' class='latex' /> and <img src='http://s0.wp.com/latex.php?latex=E%2C%5C%2CF&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='E,&#92;,F' title='E,&#92;,F' class='latex' /> the second intersections of the lines <img src='http://s0.wp.com/latex.php?latex=SM%2C%5C%2CSN&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='SM,&#92;,SN' title='SM,&#92;,SN' class='latex' /> with <img src='http://s0.wp.com/latex.php?latex=%5Cmathcal+C%28O%29%2C&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='&#92;mathcal C(O),' title='&#92;mathcal C(O),' class='latex' /> respectively. The tangents in <img src='http://s0.wp.com/latex.php?latex=E%2C%5C%2CF&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='E,&#92;,F' title='E,&#92;,F' class='latex' /> with respect to the circle <img src='http://s0.wp.com/latex.php?latex=%5Cmathcal+C%28O%29&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='&#92;mathcal C(O)' title='&#92;mathcal C(O)' class='latex' /> intersect each other at <img src='http://s0.wp.com/latex.php?latex=I.&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='I.' title='I.' class='latex' /> Prove that the perpendicular bisector of the segment <img src='http://s0.wp.com/latex.php?latex=MN&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='MN' title='MN' class='latex' /> passes through the midpoint of <img src='http://s0.wp.com/latex.php?latex=SI.&amp;bg=ffffff&amp;fg=000000&amp;s=0' alt='SI.' title='SI.' class='latex' /></p>
<p style="text-align:right;"><em>(Mathematical Reflections 2007)</em></p>
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