81 lines
5.5 KiB
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81 lines
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<h2>Right triangles with integer coordinates</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 91</h3><span style="width:300px;color:#666;">Published on Friday, 18th March 2005, 06:00 pm; Solved by 7165</span></div>
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<p>The points P (<i>x</i><sub>1</sub>, <i>y</i><sub>1</sub>) and Q (<i>x</i><sub>2</sub>, <i>y</i><sub>2</sub>) are plotted at integer co-ordinates and are joined to the origin, O(0,0), to form ΔOPQ.</p>
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<p>There are exactly fourteen triangles containing a right angle that can be formed when each co-ordinate lies between 0 and 2 inclusive; that is,<br />0 <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> <i>x</i><sub>1</sub>, <i>y</i><sub>1</sub>, <i>x</i><sub>2</sub>, <i>y</i><sub>2</sub> <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> 2.</p>
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<p>Given that 0 <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> <i>x</i><sub>1</sub>, <i>y</i><sub>1</sub>, <i>x</i><sub>2</sub>, <i>y</i><sub>2</sub> <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> 50, how many right triangles can be formed?</p>
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