79 lines
5.1 KiB
HTML
79 lines
5.1 KiB
HTML
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<h2>Angular Bisector and Tangent</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 296</h3><span style="width:300px;color:#666;">Published on Friday, 11th June 2010, 01:00 pm; Solved by 379</span></div>
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Given is an integer sided triangle <var>ABC</var> with <var>BC</var> <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> <var>AC</var> <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> <var>AB</var>.<BR />
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<var>k</var> is the angular bisector of angle <var>ACB</var>.<BR /> <var>m</var> is the tangent at <var>C</var> to the circumscribed circle of <var>ABC</var>.<BR /> <var>n</var> is a line parallel to <var>m</var> through <var>B</var>.<BR />
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The intersection of <var>n</var> and <var>k</var> is called <var>E</var>.
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<div align='center'><img src="project/images/p296_bisector.gif" /></div>
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<p>
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How many triangles <var>ABC</var> with a perimeter not exceeding 100 000 exist such that <var>BE</var> has integral length?
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