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problem 91 · 9 lines

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<p>The points $P(x_1, y_1)$ and $Q(x_2, y_2)$ are plotted at integer co-ordinates and are joined to the origin, $O(0,0)$, to form $\triangle OPQ$.</p>
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<img alt="" class="dark_img" src="resources/0091_1.png"/><br/></div>
<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, $0 \le x_1, y_1, x_2, y_2 \le 2$.</p>
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<img alt="" src="resources/0091_2.png"/><br/></div>
<p>Given that $0 \le x_1, y_1, x_2, y_2 \le 50$, how many right triangles can be formed?</p>
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