{"status": "success", "data": {"description_md": "Complex numbers $a$, $b$ and $c$ are the zeros of a polynomial $P(z) = z^3+qz+r$, and $|a|^2+|b|^2+|c|^2=250$. The points corresponding to $a$, $b$, and $c$ in the complex plane are the vertices of a right triangle with hypotenuse $h$. Find $h^2$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Complex numbers <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span> and <span class=\"katex--inline\">c</span> are the zeros of a polynomial <span class=\"katex--inline\">P(z) = z^3+qz+r</span>, and <span class=\"katex--inline\">|a|^2+|b|^2+|c|^2=250</span>. The points corresponding to <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span> in the complex plane are the vertices of a right triangle with hypotenuse <span class=\"katex--inline\">h</span>. Find <span class=\"katex--inline\">h^2</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2012 AIME I Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/12_aime_I_p15", "prev": "/problem/12_aime_I_p13"}}