{"status": "success", "data": {"description_md": "In isosceles trapezoid $ABCD$, parallel bases $\\overline{AB}$ and $\\overline{CD}$ have lengths $500$ and $650$, respectively, and $AD=BC=333$. The angle bisectors of $\\angle{A}$ and $\\angle{D}$ meet at $P$, and the angle bisectors of $\\angle{B}$ and $\\angle{C}$ meet at $Q$. Find $PQ$.<br>Leading zeroes must be inputted, so if your answer is `34`, then input `034`\n\n___\n\nFull 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>In isosceles trapezoid <span class=\"katex--inline\">ABCD</span>, parallel bases <span class=\"katex--inline\">\\overline{AB}</span> and <span class=\"katex--inline\">\\overline{CD}</span> have lengths <span class=\"katex--inline\">500</span> and <span class=\"katex--inline\">650</span>, respectively, and <span class=\"katex--inline\">AD=BC=333</span>. The angle bisectors of <span class=\"katex--inline\">\\angle{A}</span> and <span class=\"katex--inline\">\\angle{D}</span> meet at <span class=\"katex--inline\">P</span>, and the angle bisectors of <span class=\"katex--inline\">\\angle{B}</span> and <span class=\"katex--inline\">\\angle{C}</span> meet at <span class=\"katex--inline\">Q</span>. Find <span class=\"katex--inline\">PQ</span>.<br/>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code></p>&#10;<hr/>&#10;<p>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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2022 AIME I Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/22_aime_I_p04", "prev": "/problem/22_aime_I_p02"}}